1) Is there any good solution how to fix freeze at spawn? Whenever I type /spawn I get stuck in blocks for some seconds and then release from them or I just spawn normal and I need to wait some seconds so I can move around without teleporting back to spawn.
I think yes, because spawn is right on that block level. Arran or Cheeze can make spawn anywhere else by using /setworldspawn.
2) I want information about unbreaking pickaxe. Right now I have "Unbreaking III". But can I get unbreaking pickaxe and keep it forever without fixing it? But anyway what is max level of that power and how to upgrade only "unbreaking" ?
Max Unbreaking level is III. If you want your pickaxe to be undestructable, you will have to get Mending enchant on it, it's super rare. It fixes itself while you're mining.
3) Can we create shop with chests and make it so we will buy stuff only? For example I need 10 stacks of wool right? Can I create chest and let players sell their wool to me BUT storage will stop at 10 stacks. Because I don't need more than 10. Maybe some rich player comes and rapes my balance with his wools? lol
No, however you may fill the chest with other blocks, for example fill almost all the chest will cobblestone, and leave 10 gaps for wool.