Here is some tips for you!
1. Use a torch while lockpicking and it becomes easier
2. Shops and Merchants restock their gold and supplies every 48hours in game.
3. You can command your follower to pick a lock, pick something up, or even steal and etc...
4. When you break a pick or turn the lock when it's in the wrong position, the pick will "flick" towards the correct position.
5. When paying tutors to upgrade skills, you can pickpocket your cash back. It drops to 50-50 chance at about 2000 septims, or just kill the tutor for your gold back.
6. Mines and Dungeons respawn every month (30 in game days).
7. The "Impact" perk in the Destruction tree will stop a dragon from breathing fire/frost
8. Re-equiping any item with +## to Maximum Magicka on it, when your mana pool is depleted, will restore that amount.
9. Arrows are now weightless (alot of people did not notice this)
10. Fire = Damage + Dots (damage over time), Frost = Damage + half of that damage to Stamina, Lightning = Damage + Half of that damage to Magicka.
11. Lightning > Frost/Fire in regards to speed. (how fast it travels)
12. Pickpocket someone who shoots target dummies with arrows, and take the arrows they were using (usually iron or steel). Then, give them one of the arrow type you want more of. They will now shoot that type of arrow instead of the one they were shooting before. Simply collect the arrows as they hit the target dummy to get as many arrows as desired.
13. There is a book named "Kolb and the Dragon" in Whiterun. It is a choose-your-own adventure book.
There are your Skyrim tips to help you out!