Hope you enjoy your experience, and for starters, dont worry about difficulty. With more practice, you'll soon be a master at arms. For, now though, getting the hang of things is the best thing possible.
To answer
1)The quest they give you might be hard because of a couple of reasons. Your gear may be obsolete, and you may want to enchant things, it makes fighting alot easier. Make sure you spent your perks once you level up. They can be life savers. Also, the enemies will always be around your level, so it will be challenging. But the random generator may give you a couple of very hard enemies some times. Just trust in your abilities and give it your best. If you find you cannot beat them. Try practicing elsewhere, and come back later. There is no immediate rush.
2)For 2 handers the general rule is. Swords are faster than axes, and axes are faster than hammers.
3)I'm not aware of what your hinting at unfortunately, and no spoilers can be revealed in this thread, so i can't help you with that. I'd say, follow the quest, and do what seems best to you. Don't worry too much about making a mistake. If there is some kind of decision, you'll know or have an idea, of what the consequences will be.
4)If you don't want involvement in the civil war quest, there are still literally thousands of others to do. If you mean what is close to whiterun, you can do quite a bit. Talk to the citizens, most will have things for you to do. If you want to go a tad further. Check out other cities. Riften, winterhold, markarth, etc. All will have a great deal of things to keep you busy. Not to mention the numerous groups you can join.
Hope this helped you, even if just a tad.
Also hope you continue to enjoy your warrior
Good luck!