Yes, indexes is safe to copy. It only contains transaction data and is completely unrelated to the wallet. In fact, indexes used to be part of blocks so with older versions, if you had txindex=1, then copying blocks meant you also copied indexes. Only recently was this separated into its own folder in the datadir.
A wallet.dat file contains no information specific to a particular install of Bitcoin Core, or its configured data and wallet directories.
You can freely copy just the wallet file to another instance, without having to copy the block data or other information such as peers, mempool, etc.
1) If I only backup that extended private masterkey, would I be able to recreate the wallet entirely in case my application crashes? Or do I really need to backup the wallet file itself? (Let's say I do not import addresses that were not generated by bitcoind itself.)
No. Bitcoin Core does not allow your to create a wallet from the master private key. There ...