Ok, obviously this comes down to DMs discretion, but I wanted to get some other GMs thoughts. I have three related scenarios I have been contemplating related paying for traits and skills:

First scenario:
Lets say a RT really goes out of his way for a group (ecclesiasty, underworld, inquisition, etc) and you feel it is now appropriate for them to gain the peer(*group*) trait to represent that they now have contacts in that group. In my mind there are two ways to handle this:

1) you give them an elite advancement option. They may now buy that trait with their xp.
2) you give them that trait as a story re-ward

Is option 2 a valid option, or should you always make them pay for character advancements, even when earned.

Second scenario. This one is an actual one I'm dealing with right now:
A character (senchal) really goes all out in character creation. A fantastic them, well developed personality, ties to the group, and well thought out history with some great plot hooks for future adventures. Really wants to focus on the master of spies/assassins aspect of the character, and due to a lucky roll is fantastic at close combat and use the power sword left to them by their mentor. BUT, senchals don't get training in those weapons until rank 4. These are the three options I see:

1) go by the rules, it keeps things balanced, and a hell pistol is still pretty cool for a senchal
2) give them the option for an elite advancement in melee weapons (universal) or (power sword) that they can pay for
3) swap out weapon training(universal) for melee weapons(universal)

My thoughts on the first two scenarios brought me to a final one:
A PC spends a long period of time in a situation where they would gain new combat skills. Do you grant them free of charge, or make them pay XP as an elite advancement. Similarly, they spend six months doing heavy labor. Should you just up their strength stat, or make them pay for it.

Here's my train of thought:
Scenario 1: It always seemed to me that things like peers were the just rewards of adventuring, just as much as gold. Sure grant them the contacts!
Scenario 2: Well this is a Combat Skill! It has a real tangible effect on the game! You can't just GIVE players powerful skills like that. But maybe swapping is an option.

Which got me to thinking: Don't traits and contacts have just as real an effect on the game? Certainly! And I wouldn't just let them gain a free combat skill or base stat increase due to a situation. That is what XP represents after all, getting more powerful through experience.

So the hard liner in me begins to say "Pay XP for ANY gains, that is what XP represents after all."

But the storyteller in me says "If they can gain an artifact as a reward, if they can gain a SHIP as a reward, why can't they gain a contact as a reward? And beyond that, why then can't they gain skills?

Thoughts?

Having a Contact, or even a many many contacts in in a particular group is not the same as having Peer (Group Name) or Good Reputation (Group Name). For example, I may have talked at length with many Red Shirts at GW stores. This might give me contacts with Redshirts. This would not give me Peer (Redshirt) as they do not recognize me as a fellow.

Moving beyond that distinction into game theory, I have to agree with the hardline you. In theory, there's nothing to prevent you from runing a game without experance. Everytime someone does enough of RPing about somthing to train or otherwise aquire said talent or skill, you could give it to them. "I get lessions from this old Inquisitor on how to use a power sword, and practice often." "Alright, you have Weapon Proficiencey(Power Sword)."

The reason we use experance at all is to create a messured rate of advancement to maintain game equality among members. It creates at least the impression that Player A's Senichal is about a useful to the party as Player B's Arch Millitant. This helps keep the game fun and interesting for all players involved. It also creates a feeling of success and advancement in the players.

Because of all this, I personaly reqire every advance to be bought with experance, but also try to limit the number of advancements that come out of left field "because its on the list".

This, of course, only applies to individual abilities. Let us say that the party does a great favor for the Mechanicus. This could grant the group a +10 bonus to all future dealings with the Cult of Mars. Because it's applied party wide, it doesn't adjust the relitive character effectiveness balance, and therefore, can be done without the expenditure of experance. Becareful with this though, to many of these will start to make individual skills or talents feal undereffective.

For your current situation, I'd sugest the swap, or an Elite Advance (250-350xp) for Melee Training (Power Sword).

i find myself leaning towards the hardliner side, in those situations i tend to reward my players with bonus XP for excellent role play i find is save on unbalancing the game. in your current situation id go for the swap

Here's how I handle it:

If the trait is wholly and completely earned through RP, such as doing something so major that the entirety of an organization recognizes your actions as awesome, then you get the "Peer" or even "Good Reputation" for free.

On the other hand, if you've just gotten in good with the local membership, then you have contacts, and from those contacts, and excuse to buy the Peer/GR as an Elite Advance to show that you can talk the talk and walk the walk around others of the same affiliation.

Other more specific traits, such as "Oathbound to the Angels of Death", the Inquisitor in the last game I ran earned for free due to his actions on behalf of an Astartes chapter.

This might be late now for your 2nd problem, but I see another option for the character.

One page 15 of the rule book, in the top right corner there is box that discusses optional ways to use the origin path, allowing a character to make a "free choice." I could see have the players character take "Hand of War," but could reflavor it has "Hand of the Inquisition." This would allow them to start with the training for the power sword and also some enemies that may have lead to the death of their former master.

As far as you first question go, here's what I would do : give the PC the XP cost of the offered perk, which is used on the spot to buy said perk.

Technically it's the same as giving it for free, but it keeps the PC's level on par with what it should be if he builds up a power base from several such occurences.

Note that having the widespread repute associated with the 'Peer' perk, you'll need some drastic action - something with at least planet-wide effects. Which is fairly normal for a reptue extending to a whole sector and possibly beyond.

Swap out the weapons training evenly to keep people happy and things simple.

As for the peer/group, give it to him and make a note that in the future that peer/group might require some illegal favor or a profit damaging deal that the player must then acquiesce to.

Play is more important than anything in my opinion. Of course there are boundries, but I think both of these scenarios are easily doable and both will give you as the GM some interesting plot twists and fluff.