I reuse both the Sram separately sold links, and the Ultegra links. But I don't disassemble the chain more than a few times in it's lifetime.
They click back into place just fine.

Years ago, I had 10-speed Connex links. These don't click into place. Instead, they have a curved slot and chain tension is all that's needed for the quick link to be secure on the chain. So that's another reason I don't worry about reinstalling click links. Connex links got suddenly very expensive, so I quit using them.

I used various cheap methods for removing the links, but they didn't work easily on my 11-speed Ultegra. So I got the Park Tool Master Link Pliers MLP-1.2, So nice, easy and effective.
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Chain cleaning
I used to take the 10 speed chain off, shake it in mineral spirits, then shake in a bottle of detergent and water, rinse with rubbing alcohol, and relube. Nice and clean.
But now, I just wipe off the chain and relube. I still get the same approx 3500 miles either way!