As for your mod problem, that error message doesn't mean that the game won't run, just that the main executable thinks that the dates are wrong. You can fix this by opening each mod in the TESCS, then saving it, which will update the date embedded in the file. Or you can just ignore the error and run the game, it will probably work.
You do have to worry about conflicts between mods though, and with the game having been out 8 years now, and being one of the first big modifiable games, there are a LOT of mods available, which means a lot of opportunity for conflict. You basically have three options.
1) Keep it simple and hope for the best. This is a fire and forget style of modding. Download a few that look interesting, see if it works, then add a few more. The more you add, the more likely a conflict will be, and the harder it will be to track down the problem. If you are just using texture mods, check out the visual comparison at
Thepal's Amazing, Wonderful and Spectacular Morrowind Texture Pack Comparison Page, download all packs of the chosen system, and play the game. You probably also want to grab Better Bodies, which improves models and textures on NPCs. If you start adding in other mods, consider options 2 & 3.
2) Do some forum research. Read over past articles here, and on your preferred mod download site, for advice on popular mods and groups of mods which work well together. This will also give you general info, such as which types of mods to only use one of (game play changes, like levelling systems), which to be careful with (faction/ quest changes which may overlap NPCs/ scripts), which are usually okay (dungeons, unless there's map overlap). Problems are most common in the popular cites, such as Balmora and Vivec.
3) Do direct Mod research. This will be very time consuming, but is the only way to get exactly the mods you want, and be sure they will work together. There's a useful tool at
Morrowind Landmass Conflict Checker - aka MMGUM - Planet Elder Scrolls which has world map locations for thousands of mods, but requires you to do a lot of research.
You may also get some use out of :
Starting out with Mods (Self explanatory, will teach you the basics.)
Telesphoros' List o'Mods (Good forum list of popular mods)
Planet Elder Scrolls - Maps, News, Oblivion, Cheats, Downloads (my mod site of choice)
Galahaut's Morrowind Mod List Wiki / Mod Conflicts ( a reasonably up to date list of known conflicts on popular mods, there's a broken link, but you can find the image here :
http://www.mwmythicmods.com/MAPoMODSbyCyronaut.jpg)
The Elder Scrolls Nexus - Oblivion mods and community (the other popular mod site)
