I was just wondering, what advantages in the privacy field (potentially) can bring me use my software wallet. I noticed that Bisq already generates new deposit addresses accordingly, so that each is used only once. This is a very neat feature, I think.
So my question is: In what conditions is using my software wallet more private than using my Bisq wallet?
With Bitcoin core you can select the inputs you want to use in a tx. That is only partially possible in Bisq (you can select the address but there might be multiple inputs). Beside that Bitcoin core is a full node with all the benefits reagaring privacy and security. Bisq use SPV (BitcoinJ) which has some privacy issues (a bit complicate to explain all the details). So I would say if you want the best go for Bitcoin Core. Using mobile wallets or some other wallets with poor privacy / security is probably worse than using Bisq as wallet.
So if I understand this correctly, if I have Bitcoin Core running on my PC, than using Bisq wallet is more secure (although in that case the Bisq wallet is a bit redundant).
Is Bisq able to connect to mainnet through other software wallets like Dark Wallet, or Bitcoin Core only?
Correct.
Bisq is able to connect to any Bitcoin full node client. It connects to a port 8333 on localhost if it is available. I am not familiar with the Dark Wallet, but if it does not download a full blockchain it is not a full node client.
Bitcoin Core only