I'm having trouble understanding HD wallet privacy... for one thing, what if I want to send more money than I have in any of my individual derived addresses? Then I would have to use more than one, right? Which would compromise privacy, because it would show that at least two of my addresses are connected, exposing information about me, right? Like if I get money from A and money from B, then when I send C a payment she would know I was involved with both A and B. Can someone explain me exactly how much privacy HD wallets give compared to using the same address for everything?
HD wallets help avoid reusing addresses when receiving payments because you can generate a new address each time. HD wallets also make backup of many addresses much easier:
You are correct that when you send a payment from an HD wallet that needs to combine Bitcoin from several addresses (because no single address you control has sufficient Bitcoin to fund the payment by itself) previously unconnected addresses can become linked together.
There are multiple ways you can deal with this scenario to greatly improve privacy. Coin control and careful planning of payment sizing can minimize the frequency and privacy impact when this needs to happen. You can send Bitcoin from only one address when you desire the most privacy and combine Bitcoin from multiple addresses when privacy is less important to you.
Another solution would be this idea from Peter Todd:
"For me personally shapeshift adds a lot of value to Bitcoin, as it gives me much stronger privacy by using Monero as an anonymous intermediary point. Specifically, I buy Monero on shapeshift, then sell it to xmr.to, which in turn sends bitcoins to the Bitcoin address of my choice."