I'm used to synchronize my data on different machines. Depending on the data I use Git, Dropbox or Syncthing. Is this possible with Ethereum accounts, too?
Yes definitely - but in this case it is the blockchain that will keep track of your accounts balance. The account file on your computer does not track your balance - only the keys. Therefore you can use the same account file on any number of computers and it won't matter because the blockchain knows it's balance and will always report it correctly.