Is it possible to store all chunks in level to MySQL database and then send them to player? (except entities and tiles. Only blocks)
It's possible but it's such a bad idea, it would be so inefficient. Tell us what's your goal so we can give you an hint on what's the better way to achieve it.
I have adventure map on my server, I want to store chunks of this world and then load it for player that's on totally another server.
This is a normal MySQL table, How on earth are you going to store chunks in it. You're better writing a plugin that downloads the map from a server
Use a database genuinely designed for large files, or just use an online file transferring service like transfer.sh (although they most likely aren't designed for automation)
MySQL is efficient but isn't designed for what you're using it for. You can try linking world directories https://stackoverflow.com/questions/9587445/how-to-create-a-link-to-a-directory. Don't forget, you are sharing data across two servers so make sure it doesn't overlap. Have a system where only one username can be online across your network.
Do you want to sync the two worlds, or do you simply want to copy? Do you want events happening on one world to get sent to another one too?
Well, I don't want to paste world folder on my other servers because I have about 30 maps on server and when all of them are loaded on all of my servers it start lagging