Helllo. I'm rather new to modding and haven't done any mods myself yet.
I've just completed installing Morrowind Graphics/Sound Overhaul + all listed Morrowind Overhaul - Game Experience mods, because sadly they aren't compiled yet. (it literally took me a day to get it all working).
In that list there are no mods to change/fix fighting system; morrowind's combat in general. I am wondering what mods are out there that fix and improve Morrowind's combat? I know that people argue between Morrowind's and Oblivion's combat, but I would like something in between.

Well no matter, any help greatly appreciated.
Thank you.

Hello and welcome to the wonderful world of modding.

Here's a few combat mods that you might find interesting.

http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=8355

http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=6036

http://www.gamesas.com/index.php?/topic/1161892-relzwipz-realistic-combat

http://www.gamesas.com/index.php?/topic/1179276-relzbeta-gratuitous-violence/

Well if u want some combat improvement you may try out my mod Combat Redefined ,it will allow you to perform 9 moves with your weapon compared to default`s 3 moves(though only for One Handed and Two Handed Weapons at present) also contains 1st person animations.The animations may/may not be to your liking but u can give it a try It is compatible with Aeleron`s Combat Enhanced.
Forum Link: http://www.gamesas.com/index.php?/topic/1228701-relz-combat-redefined/
Download Link(Also contains video section) : http://www.tesnexus.com/downloads/file.php?id=40196

Hope it helps as for rest others can help you out as i dont know much about other combat mods out there.

Thank you kind sir. I will check them out right away, but for everybody's sake, are the 4 mods compatible with each other (so I can just install all 4 of them) or are they all separate and I have to choose one?

Also, is there somekind of mod installer? Where I can just select all the RARs and it installs them by istelf? I know I had something like it once, but it only "saw"/found 50% of the mods to install.

Thank you.

I can't tell you for certain but I'd think the answer is no, they most likely won't play too happily along side one another. You may physically be able to load them all up together at the same time but you would probably be better off picking a favorite and sticking with it for redundancy's sake as they all cover many of the same areas of gameplay anyways.

EDIT: As for installing them, most mods don't come with installers. They're might be some external programs that manage mod installations but I'm not aware of any at the moment (although I've never really looked). Maybe the program "Wyre Mash" has something along these lines for you.