> I'm naked, and I don't know what to do about it. Is the equipment I'm going to find all related to my level? (Level 1, I mean)
Yes and No. Head to Arrile's shop. There you can get the basic clothes. armor weapons etc. Many of the items in shops are fixed for particular traders, but some items are based on leveled list. For example, you wlil get high quality clothes from Milie Hasteen's Fine Clothes shop irrespective of your levels. But, items found in caves, tombs etc are mostly based on your levels.
> The grinding done to hit with longswords is a lot. Beside, most of the stuff I find just one hits me (I've found a cave with two people, one whose I was able to take care of, the other with a blunt weapon that smashed me with only one hit)
What is your skill in Long Blades? What is your Agility? You need to have atleast 40 in both of the weapon and agility to have more chance of hitting than missing. But as the skill increases, your odds of hitting also improve. By about weapon skill 55, you'll rarely miss. Try hitting mudcrabs and scribs toraise the skill.
> I'm constantly summoning an ancestral ghost, but my conjuration skill doesn't seem to get higher. It didn't get higher even a point even if I summoned the ghost like 25 times (?). Is there a bug?
Hover your mouse over the 'Conjuration' skill and see if the progress bar is filling up. Also, you need to 'successfully' cast the spell for progress in the relevent skill. Failure to cast doesn't progress the skill.
> I can't seem to find anywhere a way to ask about the missing taxpayer. Whom I should ask about him?
The missing taxpayer can be found by searching the coast west of seyda neen. He is hidden among the bushes.
> How can I improve my personality? If I try to persuade people, they just get mad at me (30 personality). I fail to understand how one should be able to improve it.
> Am I wrong, or if I don't use my major skills I can't level?
Attributes can be only raised during level up aside from Enchantments or spells. You get to raise Personality by more than 1 if you raise its corresponding skill more than a couple of times before level up. More info http://www.uesp.net/wiki/Morrowind:Level.
> How can I use alchemy and armorer?
You drag alchemical apparatus on to your character in menu mode. A window opens allowing you to prepare potions. More info http://www.uesp.net/wiki/Morrowind:Alchemy. As for repairing, just drag a repair hammer or repair prong on to your character. Note that you need to have atleast 40 in those skills to be decent at that.
PS: Looking at the screenshot, I see you already got clothes and armors. Just drag the robe/clothes onto your charachter and he wears it. Also, another thing I forgot. Keep an eye on fatigue. If you have low fatigue your chance of success at things drops. So don't run to places or at least avoid running just before combat.