The inventory is part of the stats/map menu, so if it doesn't appear when you open it, it's possible that it's deactivated. Once you've opened the menu by right-clicking, try clicking on the weapon you have equipped. That should make the inventory appear (if it's not a bug). There's also a magic menu that (since you didn't mention it) you may need to reactivate the same way (by clicking on the field right to equipped weapon).
The map in the menu should have a button allowing you to switch from local to world map and back.
Btw, there is also a button in the above right corner of each menu part that let's it stay on even if you close the menu (I found that useful for the map when using a detect spell).
Morrowind is a rather difficult game. In the beginning your skills are low and so a battle can easily be lost (especially since enemies do not necessarily level with you and may therefore be difficult if not impossible to beat early on).
Make sure to equip items regarding your skills (e.g. if your highest weapon skill is Short Blade, using a short blade weapon works better than using an axe).
If you face to many defeats and the game is more frustrating than fun, remember that you can lower the difficulty if you haven't done so before.
For more tips guides like this are useful:
http://www.uesp.net/wiki/Morrowind:Starting_out
In each trader's dialogue you can find the option to barter. Just see on top of the topic list on the right. For all normal characters you will find Persuation (bribe, taunt, etc.) and for some the option to trade or train (there are a few selected characters that you can't persuade). Just be aware that not all traders/trainers may be willing to deal with you right away.
And traders only have a limited amount of money, so selling more expensive things may become difficult later on (unless you know where to find the most lucrative traders (Creeper and Mudcrab))