I'm sorry, I don't have my books with me.

Do support specialists get the option at 2,500xp/5,000xp to advance a characteristic score by +5?

I remember reading somewhere that they were restricted from taking advanced specialties... or something to that effect.

Thanks.

If they dedicate, yes.

Or, alternatively, they can advance to an Advanced Specialisation for which their particular Support Specialism is eligible, for example the Pracentor of Penance Advanced Specialism for Priests.

Right now, Commissars, Psykers, and Stormies MUST dedicate, as they have no Advanced Specialties that apply to them; here's hoping FFG still has this book in them. Everyone else should have other options, be it respeccing into a new class (Heavy into Sergeant), snagging an Advanced Specialty (Sergeant to Commander or Priest into Incinerant Priest), or dedicating is still an option.

^ Unless you want to use my homebrew. Does need playtested lol. *Shameless self promotion.*

Which hombrew, laz? Last I checked you had fifteen....hundred to choose from.

The Tempest specifically. It's under the House Rules section. Covers the following;

Tempestus Commissar (Spec ops driven advanced specialisation.)
Lord Commissar (Skills/Social driven advanced specialisation.)
Exemplar (Melee combat driven advanced specialisation for Commissars.)

Primaris Psyker (Blasty focus Psyker advance.)
Sage (Skills/Defensive/Supporting Psyker advance)
Battlemind (Melee oriented Psyker advance, Dark Heresy rules for Force Weapons advised.)

Tempestor (Stormtrooper Sergeant specialism)
Saboteur (Sneaky, Tech-oriented Stormtrooper advance.)
Assault (Full blown combat vanguard advance.)

There's an Assault about to see action in a game this weekend, but none of the others have been live tested, so I'd be interested to see if they perform in the field and if any tweaks need to be made.

Sadly, my game is dealing with a Penal Regiment and the PCs were restricted on some of their specialty choices. Needless to say, we have no Commissars, Storm Troopers or Psykers.

That's completely understandable! Perhaps in the future!

^ Unless you want to use my homebrew. Does need playtested lol. *Shameless self promotion.*

Is the Navy-thingie close to playtest ready.

And where can I find it?

It's close. Not pretty yet by any means, though. I'm going to need to fill in the blanks on the talents, tidy up the aerial combat rules to cleaner English. We're not quite done yet with NPC pilots or xenos craft though, unless you'd like to just use a generic Ork/Severan/Eldar X and give it Operate (Aeronautica). We need a bit more time for that.