On the downloads section of this site each scenario should say what version it works with. As a general rule though look at the file name and see if:
.AGE3SCN: works with any version
.AGE3XSCN: only works with TWC*
.AGE3YSCN: only works with TAD*
*these scenarios could have objects from the other expansion so require both expansions to work.
This is less likely with AGE3XSCN as TWC was released first, and more likely with TAD as it was released later so many people had both TAD and TWC when working on TAD scenarios.
As for mods to install them just follow the instructions the mods should give in thier download file.
some mods can modify certain game files that will not allow you to play with other players online (this will say 'CRC mismatch' on ESO) unless they have the same mod as you . A good example of this is the fan patch, as you can play people who have it installed but no one else.
Other mods will not change who you can play with, most utility mods (eg. UI changers, reyks editor) are like this.
Generally most scenarios are designed for and should be played with an un-modded version of AOE or expansions. Most scenarios will play with mods (I think) but gameplay may be affected.
Only scenarios designed for the a specific mod should be played with them.
hope that helps