Is there a good overview to find connector types?
since you don't care about every connector that might have existed, but only those you can actually buy, the kind-of-logical-ain't-it answer to your first question (list?) is:
Go to one of the large electronic distributor's websites, click through to the connector listings, and select filters that describe your connector.
Regarding your second question (ID this connector?): a 24-contact mezzanine rectangular connector, photographed very much out of focus ;) (more pixels don't help if they aren't sharp; try photographing at a larger distance next time). I'd do exactly the same: I'd have to go to a distributor website, click through to the rectangular connectors, and peruse the filters until I found few enough potential matches. You can do the same, AND you have the connector (or its remnants) at hand, so you stand a better chance than I do to find the right connector.