I changed the tags of my old chess posts to integrate them into the new community, but currently I cannot see them there.

This doesn't work. Hive id tag MUST BE the primary tag, at least until roadscape figures out a solution to deal with other aspects like resteeming or cross-posting, which may require this to be reworked.

Do you want a solution to that? Create an index post in your new community, and add the links to your older posts in there. You can even pin that index post. I do that at SteemHelp.

When searching for communities, one should be able to find ALL of them.

That is true. However, when I checked a few weeks ago there were over 500 Hive communities. Might be close to 1000 now. It's not a good solution to list them all, especially since the number will only grow. This will probably be fixed when search and filters will be introduced. Right now only active communities are displayed. Not sure myself how "activity" is defined, seems to be a combination of number of subscribers and posts / comments from different people. Right now the only way to find a community which isn't listed in "Explore" is through direct link. Then remember to subscribe and it will be in your list.

I wonder how to sort the list of the people I follow in an alphabetical order, so that it is easy for example to find certain user names in case one is not completely sure anymore how to spell them?

About sorting people you follow or followers that's a good suggestion for general interfaces, which list them in the reversed order of follow; you can search or see them ordered from SteemWorld.