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That's awesome. I definitely want to move to decentralized exchanges ASAP to minimize the trust required for these kinds of transactions.

Does that mean you also have to pay transaction fees for every trade, and wait for confirmations, etc.?

Correct, whether it's worth it or not depends on how much you care about security and decentralization. It works well for OTC trades, dark pools, escrow, no-limit withdrawals(because you're trading from your own wallet), and anyone who doesn't want to create an account and have their trades tracked.

What are the tax implications of owning your own coins when trading, compared to someone else owning the coins but giving you rights to it?

Identical