Setting up lightning with bitcoin-core I have some questions about bitcoin-core and lightning-network-daemon.
I have succesfully set up a bitcoin node running on Ubuntu Server 20.04 by following this tutorial: https://bitcoin.org/en/full-node. 
This is my node: https://bitnodes.io/nodes/81.166.125.218-8333/
I am planning on installing lnd using bitcoind as the backend, by following this tutorial: https://github.com/lightningnetwork/lnd/blob/master/docs/INSTALL.md
In this regard, I have the following questions:

What is the relationship between my bitcoin-core wallet and the lnd wallet?
What fee should I set to make my lnd node as profitable as possible?
What other recommendations can you give to help out a bitcoin- and lnd-noob like me?

Thanks in advance for all answers! 
Best regards
The Bitcoin Core wallet and the LND wallet are completely separate wallets. LND relies on Bitcoin Core as a source for the blockchain data, nothing more.
The profitability of your node depends on where it is situated in the network's topology. If you want to run Lightning to earn money, you will need to pick reliable nodes as channel partners, but also try to connect some distant parts of the network, or situate yourself on shortest paths in other ways. I don't think it's possible to give a blanket recommendation for fees. You may find this talk from the Chaincode Lightning Residency useful: transcript, video. Then maybe just start with the defaults, look around what others are doing and experiment a bit. You could also pop into the Lightning slack and ask the present experts for advice on that.
Generally, just play around with it a bit, don't worry too much about the proft when you're just getting started. Familiarize yourself with the wallet setup and figure out the backup situation (static channel backups) first. Don't put too much money on the line, it's a hot wallet.