There is an Inquisition Codex - should I get this one or the Militarum Tempestus one?
I've never used it, but I do have the Inquisition Codex, so I'll try and give a bit of a review.
There's three HQ options, one for each of the Ordos (plus rules for special characters Coteaz and Karamazov). Each has the same stat line (and dirt-cheap cost), but different equipment options;
- The Ordo Malleus Inquisitor brings Grey Knight toys like the Nemesis Hammer, daemonblade and psybolt ammo, as well as more standard things like plasma pistols, combo-weapons, and powerfist/powersword. Also he's the only one you can purchase Terminator armour for.
- The Ordo Xenos Inquisitor gets the needle pistol, conversion beamer, digital weapons and a couple of other options. He's mostly geared towards shootiness (but can still contribute to melee with his grenades and his Poisoned (+2), AP- Scythian Talon), while the Malleus Inquisitor is geared towards close combat. Comes with carapace armour or power armour.
- The Ordo Hereticus Inquisitor has the Psyocculum, Null Rod and Condemnor boltgun, making him very good at taking out Psykers. Otherwise he just has the normal options every inquisitor has- plasma pistol, combi-weapons, power sword/fist, thunder hammer etc.
Each of them can be upgraded to a lvl1 psyker with the Hammerhand or Psychic Communion power, or a roll on the Divination, Pyromancy or Telekinesis table.
As for troops, you only have one Elite unit to choose from, but it is extremely versatile; its unit size is 3-12 models, and you can select those models from twelve different types;
- Acolyte, the standard shooty guys who start with flak armour and lasguns, but can be given power armour and storm bolters (making them essentially T3 Deathwatch, if you like)
- Arco-Flagellant, the melee guy
- Crusaders, also melee guys but focused on defense
- Daemonhost, the get-a-different-power-every-turn guy
- Death cult assassins, fragile but with a 5++ save and two power swords each
- Jokaero, who have stupidly powerful ranged weapons (counts as lascannon, multi-melta or heavy flamer- your pick, and you can pick again each turn). Also they boost your unit's shootiness by rolling on a random table each turn.
- Ministorum Priests which can take a Ld test to boost your unit (while swinging an eviscerator)
- Mystic, whose only job is to help other units with their Deep Strike rolls
- Psyker; makes the unit a brotherhood of psykers, and gives them a psychic power
- Servitor; needs an inquisitor in the unit to be effective, but can take a free multi-melta or heavy bolter (or a plasma cannon for very low cost), or you can just keep them Sx2, AP1 servo-arms for melee combat.
You can take one or two HQ choices, and up to three Elites. Each unit can take a dedicated transport; a rhino, razorback, chimera, valkyrie, or land raider (standard/crusader/redeemer).
So in short;
1) The inquisitors have the same rules and stats, but different equipment options which alter their role significantly
2) Yes, the Inquisitor Codex inquisitors are battle-brothers with all other Imperial Codexes. The Inquisitorial detachment consists of 1-2 HQ, and 0-3 Elites
2a) No veterans, but you can use Acolytes with lasguns/bolters/storm bolters and flak/carapace/power armour. Sadly, they are BS3 rather than 4
2b) No stormtroopers, but see the list of troops I described. Acolytes can have hot-shot lasguns, by the way!
Hope that helps
! Unfortunately I do not have the Tempestus Militarum list, so I can't comment on that one.