Thanks. Well it isn't the best gaming rig out there, But its good enough for me to play Skyrim on medium settings.
Secondly, the map isn't something that I am quite use to. Well the only MMO that I have played, World of Warcraft had an actual map I could see. It wasn't just a line on top of your screen. It was more of a circle if you know what I mean. Is it easy to navigate?
It sounds like you're talking about the compass at the top of your screen, that is not the map! Press M on your keyboard to bring up the map.

Pressing L will toggle you between the interactive map of Skyrim and a local map which can be helpful if you are navigating through a cityspace or large interior.
Thirdly, I don't really plan on using any mods due to people's various experiences with them such as they either cause them to get crashing, losing their save, etc. And I prefer to play the game the way it is.
With a less powerful gaming rig you may not be able to add a lot of high end textures or add a lot of extra "stuff" into the world that has to be loaded up, but there are also some mods that change other gameplay things you find annoying or fix various bugs. I would suggest the Unofficial Patch as a must have, because it has tons of bugfixes that you really don't want to play without.
But in general I think it's usually best to play for a while and when you find things you WANT to change, then you can go looking for mods that will do that for you.
Lastly, can I sell every item I pick up from guards, tankards, etc? Cause IIRC they didn't display any gold value on the screen.
Most clutter or loot that you pick up is sellable however at the beginning of the game you will find that a lot of low value items will show with a value of 1 or 2 septims in your inventory but no merchant will pay anything for them, leading to a value of 0 when you are in the buy/sell menu with a vendor. You will need to increase your speech skill and/or take some perks in that skillset in order to get an increase in what vendors will pay for your stuff (the same things will also lead to you getting better prices on their stuff)
My advice is that you not bother picking up anything that shows a value of 1 when you look at it unless it's something you plan to use. If you have to pick it up to see the value in your inventory (and you should be able to) and its value is 1, just drop it if you don't intend to use it in the near future. There is a limit to how much you can carry and there's no point in loading yourself down with stuff that you will not make any money from and have no use for otherwise.