There's no need to count, the homepage says how many active problems there currently are, in the database.
Re the duplicates, it's not terrible, at least in my opinion, to have a sub-position from a problem as a standalone problem. But it should probably be limited so that people aren't annoyed basically looking at the same situation. Just the other day, I've made
http://goproblems.com/22914 then thought I could make it slightly more interesting by removing some stones which led to
http://goproblems.com/22915 - I didn't delete since I think that the basic (like 20k) problems on the site could have some variety. But even here, I wasn't sure if I'm pushing it and maybe should've replaced it or deleted it... Exact duplicates like you've mentioned, however just seem pointless and add a bunch of work for the mods, like BartTM mentioned (BTW, Bart, thanks for trying o keep it clean, while the rest of the mods are sleeping
). Adding pointless stones doesn't help either. I just cleaned my solving history last week and went through about 30% of the problems on site and there's a ton of duplicates in the easier problems, which made this much less interesting than I'd hoped it would be...
If you want to make some problems, I suggest looking at some random games for inspiration. You can surely make a problem for every couple of games you watch that people will find interesting! If it's a bit hard at the beginning, you can checkout 9x9 games on online-go.com for ex. since the AI there reviews stuff and shows some variations. If you find some interesting variations towards the end game, or around a groups life/dead, it'll probably be easier to cover them well enough for a problem.