The advice hyunkyl gave you is pretty basic but true in every aspect. As for a point for point response to your questions, here goes.
1. Is the best way to gear thief for TP still haste gear? Is the haste cap from gear still 25%? Should I still focus my gear around haste and low delay weapons?
Yes, and unless SE changes the mechanics of haste, that should always be true. Yes the haste cap is still 25% (or 26% if you are actually speccing the math out). Yes and no. Extremely low delay weapons are not as heavily sought out as they once were. There is a really nice 150 delay dagger with +5% triple attack on it, but I think it drops from legion. Most of my daggers are between 186 and 201 delay.
2. What is the best dagger nowadays?
I see a nice 51 base damage dagger on the AH, but it has a delay of 200. I know that a fire thokcha is a good weapon and the base damage is 47 with a 190 delay.
Should I build my set around haste and then get the high dmg, high delay daggers until I can get the trials weapons? I haven't started any trials yet.
Best dagger is either Mandau or Twashtar probably. Twashtar is easier to build up to level 85-90, but with the changes in the last few years to dynamis, Mandau is not a pipe dream anymore.
Off the AH, hyunkyl recommened two very good daggers. Aluh Jambiya is what I am currently using in my main hand, and I keep an Oynos for situations where I am soloing, cause being able to self haste is awesome. Another good AH option is an Oxossi Facon/+1. They are really expensive, but can tide you over while you get other non-buyable options.
In terms of non-buyable daggers, you will want to make probably at least 1 thokcha (trial of the magians). I recommend the STR path, there have been times I have wished I had also done an AGI path thokcha too, but they are few and far between. Also from trial of the magians a Centovente with TP bonus +100 has it's uses for offhand Twashtar and Aeolian Edge, but not a priority.
There are also a few rare/ex daggers that are nice, but.... good luck on those. They are Asteria/Blustery Dagger, and Coruscanti/Lux Pugio. They have abysmal drop rates.
3. Is the raiders gear I can get from abyssea better than most gear nowadays? I see a lot of decent looking gear on the auction house, is it still considered "gimp" to be an auction-house-thief like it used to be? Some of that gear on the AH looks pretty good actually.
The raider's set is a good set. It is not the best, but it is better than anything on the AH and a good starting point. As an initial goal, you should look at getting all 5 +2 raider's pieces. Head/Body/Legs will be part of your haste build along with a Twilight Belt and one other piece of haste gear. That could be Baillerines on your feet or Ocelot Gloves, or even Dusk Gloves if you don't mind the movement down or being responsible for switching hands out after battle. Raider's Hands +2 are your best evisceration and Sneak Attack hands by far. Raider's Feet +2 are great for Exenterator (merit weaponskill for dagger) and evasion build and +1 treasure hunter. Also of note is the Raider's boomerang.
Once you get your raider's set built, then you can look at the more high end armor sets like Thaumas from Neo Nyzul Isle, or Skadi +1/Sigyn's sets from the Neo Salvage event.