I'm wondering do smaller states and realms within the empire or "outside" of it like the hutt space still have official navies or only patrol crafts and "pirates" ?

(I'm wondering if palpatine forced them to completely disband their individual navies or not)

The Hutts have self-government over what's called Hutt Space. There's also the Corporate Sector, and (I think) the Tion Hegemony. Oh, and Hapan. These all have their own navies and handle situations that might arise within their own borders.

Other than that most systems have some patrol vessels (often not equipped with hyperdrives, so they pose no threat to the Empire) in order to keep pirates, slavers and the like at bay.

The Bothans have warships, but IIRC, they are general small and fee in number.

Yeah, it varies from gov/sector to another depending on what EU you like.

The Corporate Sector Authority has a pretty significant navy composed of older ships like Vic Star Destroyers, marauder corvettes, and upgunned medium freighters-turned patrol craft.

Tapani royal houses run smaller navies composed of mostly frigate class and below, many of local make.

Other planets/governments will be similarly low key. Usually something like a neutron star class cruiser or two, or perhaps a couple frigates, maybe a half-dozen corvette class's ships and a few dozen patol boats.

Fighters will vary depending on the resources and fleet available. Smaller gov will use them to extend their reach more then fighting, deploying them from ground bases and using them kinda like flying motorcycle cops. Places with more money, and manpower like the CSA or a more coreward government will reply them more conventionally.

Bonus game tip: locally manufactured fighters can be quickly stated using the TIE fighter as a base. Just lower the speed to 4, the handling by 2, and then add other systems like weapons or shields.

Actually the Tapani Assault Frigate, like most Star Wars ship models called Assault Frigates or Star Frigates is a heavy cruiser sized hull not a frigate sized hull. The Tapani Assault Frigate will almost certainly be Sil 7 because its slightly larger then a Vindicator while the actual frigate sized ships which have appeared in the RPG are Sil 5 or Sil 6.

Yes

But mostly for system defense and patrols. About the equivalent of any coast guard.

Maybe one or two or cruisers as a flag ship. The rest would be corvettes, frigates and systems patrol craft.

There are also mercenary forces, including those that are only technically mercenaries working long-term exclusive contracts for a single employer (government or corporate).

The Bothans have warships, but IIRC, they are general small and fee in number.

I on't know about them being few in number or small anymore. A couple of years ago I would have agreed with you but the Essential Guide to Warfare has a map showing major capital ship production centers dated a few months before Endor and it lists Bothawui as a major cruiser production center. I doubt they produce warships in the numbers needed to count as a major production center and don't have a good sized fleet of them.

The DAC system has a large enough navy to free itself from the empire.

True and they built a new hidden shipyard nearby as well though I believe that was built pre-revolt given how long it is supposed to take to build a shipyard from scratch.

I think the Bothan yard and the two Mon cal yards were the only major warship production centers listed that weren't controlled by the empire, or an imperial allied state or vassal state before Endor.

My understanding is that, under the Old Republic, most sectors and major star systems had their own navies. Under the Empire, many of these have decayed as the Imperial Navy grew but there are a few exceptions... mostly in the Outer Rim and depending on how Imperial a sector or system is. The AoR core notes some of these near page 372. Core worlds may still have a considerable local force (i.e., CorSec) if they were able to pay their Imperial taxes and fund their own.

You Know What, Its Your Game. If You Want To Let A Planet Have A Small Navy, Give Them A Small navy

Short answer:

miishelle has some point - if you need a local government ship in a game, go ahead and put one in. Although the Empire did have planetary defense restrictions, none of them were strong enough or well enough enforced to compleatly eliminate the local millitary forces.

Longer answer:

It was the Clone Wars, rather than imperial decree, that eliminated the system and sector defense fleets in the first place. The Old Republic was not unlike the united nations - it could pass actions against someone, but had no millitary to back up those actions. It was compleatly dependent on the millitary forces of it's member states sectors. Powerful sectors like Kuat, Corrillia and Aldaraan would provide ships and men who would be deployed under Republic colors. The need to fight the CIS reqired far more millitary power than just the Grand Army of the Republic could provide at the onset. As such, they essentaly drafted every member sector's navy into the GAotR. These ships would eventualy be phased out in favor of new vessels like the Venetor and Victory, but the Clone Wars bascily eliminated the local defense fleets.

Faced with few defense fleets to deal with, the Empire issued laws restricting the creation of new defense fleets beyond that nessisary for local law enforcement. Of course, what that means varied from sector to sector and planet to planet based on the nature of the sector govenor, the wealth and influance of the planet, and other local conditions. Kuat and Corilla were known to have major local fleets, while Aldaraan symbolicly eliminated their compleatly as a form of protest. On other worlds it would vary from a handful of starfighters to handful of cruisers.

As for independent sectors/systems/areas - Hapes is one. Corperate Sector was semi-independent - they were answerable to the Empire, but were trusted to handle all their own issues. Hutt space is not actualy politicaly seperate - nor were they under the Republic. Hutt space is more of a sphere of influance diagram then a political situation. The Imperial Govenors assigned to sectors in Hutt space, however, were often fighting an uphill battle, if they wern't on the payroll of the kajak entirely.