That means running your own node and parsing all new blocks by yourself. That's not something I can do (yet).

I don't really mind waiting a few minutes for certain things. In fact, I often download 800 MB now just to check a few addresses. A better system would be to only download changes after the initial download, so it would be much faster.

When I tested your site with 30 addresses, I got only 9 results. It was fast, but incomplete. But what if you want to check 10 million addresses? Or even just 10 thousand? As far as I know, there isn't a single website that can do this, while there are already a lot of websites that tell you the balance of one (or a few) addresses.

When I do a local search to find matching addresses, it doesn't really matter much for the search time whether it's 1 or a million addresses. I'm pretty sure using a database would be much faster to get one address, but I don't know if it can beat the speed of searching a text-file for a million matches.

Let me know if I can help, just know I still know nothing about databases

I'm pretty sure most people who want to get balances of (say) a million addresses are trying to brute-force private keys. That means All Bitcoin addresses ever used to keep any private key that has ever been used. I know there are people who brute-force for instance brain wallets, but I don't know what they use to check the address history for many (millions of) addresses per second.

You can do this with Bitcoin Core without this privacy problem.

Not all the information you send has to be yours, you can easily add some other read-only addresses to your list. Some fake information can improve your privacy (but it won't make it easier to see the total balance).