I have 2 questions for experienced players in Skyrim:

1- Is there a maximum number of skills not to be too weak? I'm currently going with 6: One handed, Destruction, Restoration, Heavy armor, Smithing and Enchanting. Is it OK?

2- There are lots of skill books everywhere that does not have a sign to indicate which skill they increase. And I accidentally read some of them. Is there a solution for this?

You can usually guess from the title as to what skill the books increase. Before you read them, check their value - the skill books have a higher value of about 50 gold or more.

Those six skills will do you just fine, people only tend to become 'weak' if they train non combat skills too much, such as pickpocketing, lockpicking and speech, so that they are technically a higher level, but their combat skills don't match that.

But we also have to use lockpicking and speech(selling items) since we have no alternatives I guess? Or do you avoid picking locks and selling items? :confused:

It's not that bad honestly, it only really becomes an issue when you've got someone who has spent all their time thieving or what have you, and then they're suddenly level 20 but they haven't leveled their combat skills at all. As long as your combat skills are about level with the rest of your skills you shouldn't have a problem.

Im working on getting sneak, archery,andlusion up to 100, they are my main skills.One handed trails not to far behind, I just dont use it as much as archery.I also lvl smithing( I know, cheap, but I have to keep my followers in the game at higher lvls by giving them better stuff,pluss, glass and dragon stuff look very good on my character :hubbahubba: )
I also lvl alchemy and pickpocketing,though I usualy take only the first rank of thier first perks. Then lockpicking and speech sort of lvl them selves up as I play, though kind of slowly since I dont focus on them. The rest of the skills I dont realy use that much.