My reputation score seems to be stuck at 510 even if some of my answers were up-voted recently. How do I fix this bug? How do I contact the moderators in order to solve (or at least understand) the problem?
That's a community wiki answer, and you don't get any reputation for upvotes on them (nor do you lose any from downvotes). The idea behind this is that they're easy to edit (for everybody with at least 100 reputation) and are a collaborative effort, and therefore do not confer reputation. Since at the moment it's 100% your work, this might not be fair, but it's hard to make some kind of system to 'correctly' distribute reputation among the contributors.
Usually, you have to explicitly indicate you want your answer to be a community wiki; however, this is a community wiki question and all its answers are automatically community wiki as well.
How do I contact the moderators in order to solve (or at least understand) the problem?
Well, you did the right thing: asking here on Meta. This has the benefit of being a semi-interactive format, visible for more users than just the moderators, and increasing the knowledge of other users about how the site works.