Hello forum I will be starting a Rogue Trader Campaign and I was wondering. Would the Administadum keep watch and give orders to Rogue Traders? I wanted a misterious person telling them specail things to do every no and then? any ideas???

The Administratum is likely to check up on their progress every now and then, but that's likely restricted to basically making sure the Seneschal's doing the Rogue Trader's taxes properly and the Imperium's receiving their correct tithe. A Rogue Trader has effectively no ruler while out in the Expanse. That said, there's no reason some powerful figure wouldn't occasionally dangle a promise of profit and glory in front of his nose, in exchange for a trifling little task.

There is probably going to be at least one Inquisitor watching the Rogue Trader, even if that means they occasionally abduct a high ranking crewmember, mind scan him, then replace memories of the scan with memories of a pleasant but uneventful shore-leave.

There is the ship past history option where they bought the ship with a loan, meaning they owe a lot of money to someone rather powerful.

There's fluff in the book that suggests whoever gives out the Warrant of Trade may well be keeping agents on board the ship to keep an eye on the Rogue Trader. Also the Warrant of Trade is not a standard document. Many - if not most - of them have provisos about visiting certain planets, duties the warrant requires, lending aid to the Inquisition or Imperial navy etc etc. Pretty sure there's mention of Imperial Assassins being hidden aboard the ships to kill the RT if he gets out of line.

In answer to your first question...it is complicated, but the most simple answer is no. But there are some yesses in there too.

First I'll explain the no:

Rogue Traders are one of the primary branches of the Imperium, and like the other primary branches (High Lords, Space Marines, Inquisitors, Ad-Mech) they have NO superiors except the Emperor. In their area of authority they speak with his authority. A Rogue Trader is the equal of an Inquisitor or Space Marine Chapter Master. No one can give them "orders".

Due to the seperation of powers within the Imperium the heads of the various branches have to be careful and show respect. If an Inquisitor is keeping tabs on them it should probably be descreetly. Anything as obvious as abducting crew without cause is going to case an outrage among the Rogue Traders as it is a threat to their soverenity. It is like if an Inquisitor randomly started abducting Space Marines, soon they would have dozens of chapters coming down on their heads.

Likewise the book indicates that the administratum and even the High Lords of Terra can't directly order the Rogue Trader around. According to imperial law and ecclesiarchy custom the Rogue Trader largely untouchable unless they really step out of line within the Imperium.

Within their area of authority (outside of the Imperium and not actively becoming traitors) they have unlimited power. Of course within the imperium is another thing entirely.

Now I'll explain the 'yes's:

The only thing controlling a Rogue Trader is their Warrant of Trade. To circumvent their unlimited power a Rogue Trader "Warrants of Trade" often have special conditions written in to them. There are some great examples online (an especialy good one taken from an actual sixteen page dutch warrant of trade). You can use these special conditions to excersize authority over them. A few examples I have seen (and used):

-The (Imperial agency, i.e. inquisition, administratum) may require the assistance of the Rogue Traders military x times in a y year period. ( I did 5 times in a 30 year period, with 2 times used on the players predicessor)
-The bureaucracy of the Imperium has the right to audit the Trader's books every x years. (remember, they will be taxing the Rogue Traders gains)
-The Rogue Trader will turn his books over to the bureaucracy every x years for this audit, and if by the end of x+10 years, they have heard no word, this Warrant of Trade is revoked.
-The Rogue Trader's vessels must return to their home port, and if they end up at another port, all profits and materiel must be shipped TO that port for audit and taxation.
-If the Sector Governor sends someone to collect a tithe from any planet the Rogue Trader has claimed in the name of the Imperium, the Rogue Trader is obligated to provide access to this world.
-After any journey, the Trader or his organization must file an Astropathic report with the Imperium, as well as a written log with the local Administratum.

The warrant should also be empowering. It is both the source of their power and their anchor back to the imperium. Some empowering conditions:

-Should anyone cause greivience, damages, or hinder the lawful trade of the Rogue Traders Dynasty the Rogue Trader is empowered and commanded to (fancy words for MESS THEIR FACES UP!!!)
-The Rogue Trader may call upon the assistance of the imperial navy in exacting justice in the form of (fine print here i.e. x cruisers, y escorts, etc.). (fine print on how booty will be split betweent he navy and the RT in such a case)
-Except where explicitly written in this warrant of trade the RT is beyond reproach and speaks with the voice of the Emperor within (list areas designated i.e. Koronos expanse, halo stars, Calixus sector, etc.)

Unless you have an excellent story reason to do so I wouldn't give anyone direct control over them. If you put conditions in their warrant that give people control it should probably the a rare thing with well defined limits. A big part of the game, and what makes it distinct from DH, D&D, and most other games is that feeling of power and authority. If someone tries to control them it should be an event, not the norm. Something frustrating and to be avoided, not a part of daily life. The Players should be able to revel in their power. This is a game of empires, not men vs monsters.

To answer the second part of your question:

As has been mentioned, the book speaks of 'creditors', which can be a good hook. Or there can be someone who holds special sway over them due to blackmail, or a sworn oath. Or just an excellent contact.

However the best way might be just the trading of favors. A prudent RT understands that a huge part of their power and Profit Factor come from the oweing of favors, which can be more valuable than money. If a Grand Magos, Lord Inquisitor, or Lord Admeral respectully approaches them with a request it would be wise to take it and thus indebt that organization to the dynasty. Likewise the Rogue Trader may OWE favors to certain individuals and organizations, and reneging upon them would make the Trader lose face and power.

I favor this last solution as it maintains the Rogue Traders power and independance while still providing direction to the campaign. It is more in line with the feel of being an all powerful Rogue Trader dealing in the politics of the Imperium.

Riplikash nailed it but i'll add a further point.

Just because no one has lawful authority over a rogue trader bar the Emperor and any conditions in the Warrant of Trade, doesn't mean that someone doesn't have unlawful authority.

Now an old and powerful dynasty can pretty much stand tall against most threats, but what about a very young or impoverished dynasty? One could imagine such a rogue trader being a ripe target for powerful people needing a powerful catspaw.

e.g.

Inquisitor Jim gets in contact and presents a list of clearly false charges, then offers them clemency if they do just one little job.....

Sector Governor Bob sends a representative who requests some service in return for the governors good graces, the not-so-subtle threat being that the RT will be hassled by bureaucrats in the sector if he does not comply.

A more powerful RT dynasty suggests a joint venture, with a few gentle hints that should they anger the other RT by refusing, well, its a dangerous place the Koronus Expanse, all kinds of accidents can happen out there.

If you just want a shadowy figure who watches and drops hints rather than someone who demands, then the scope widens even more.

Chapter masters want some services done but don't want to be connected to it. Looks for a RT to help them out.

Imperial Navy are concerned about warships in their turf, send spies or surveillance ships to keep and eye.

Inquisition is worried about xenotech smugglers, infiltrates a whole bunch of RT dynasties to keep tabs on them.

etc.

As others have said. It specifically states in the book that it is rare for a warrant of trade to be given without conditions on it. That's in the chapter on Rogue Traders where they talk about motivations for becoming a rogue trader and what is common for after they attain one. The way I'd work it in is to make it something about the ship as well as the warrant. My group has the reliquary of mars trait. So from time to time adeptus mechanicus people will visit the ship and cause problems. If you did turbulent past and connected it to the Inquisition and then added something on for the warrant of trade that would probably suit your needs without bending any of the fluff bits stated in the book.