Dire Avengers were the Biel tann aspect warriors in troops slots. They still are. They are squishy in the current game meta, and will probably require wave serpent transports if you want to keep them alive longer than turn3.
Currently there are not a lot of specialist Eldar lists (that are "legal"). The main codex covers a lot of the older rules in a watered down way. There is a Wraith book (Iyanden supplement). The old Biel tann is covered in the main book.
The old 1 HQ + 2 troops is a basic Detachment (with 1 more HQ, 4more troops, 3 more EL+FA+HV optional) you can add an ally of 1 HQ 1 TR (with 1 more TR,EL FA,HV optional)
Formations are easy to explain: they are basically a small group of units (usually with a theme>> like a terminator strike force) that if you buy the required units ( sometimes with restrictions >like they have to be full sized, or have transports) you get a few bonus rules for them for free.
Sometimes these rules are just basic Special rules like tankhunter (rerolls vs Armour pen) but they can also be specially written for the formation like the marine Double demi Strike force (Full Marine battle company 2 commanders 6 troops, 2 FA, 2 HV and you get free transports....
In the current game you can field a Std Detachment (to get Objective secured for your troops= they will hold an objective even if enemy units are there, unless the enemy also have objective secured rule).
You can also just field formations/allies if you want or a combination. (some formations can be as small as 25 points worth of stuff).
You can even have a fields any units (so called Unbound lists) but no one I know actually does that, unless it has been agreed upon beforehand.