Hello,
that is quite an odd issue. Just to confirm, are you using the Windows client or the Web client?
Have you noticed that no shortcuts work at all, or just the ones you have listed? For example have you tried CTRL+F to open the friends list?
If it's only the mentioned shortcuts, a silly thing, but make sure that you are pressing the shortcuts in the menu list box, not in the chat edit field or the history box, as that won't work. For CTRL+R in particular, you can only reply once you open the topic, you can't press CTRL+R on a topic in the list of topics.
If you use NVDA, try to first press NVDA+F2 (a command to pass the next key directly to the application), and then immediately press a shortcut which doesn't work such as CTRL+R. If it works after you do this, it suggests one of the NVDA addons is globally taking over the shortcut in some unexpected way. I haven't encountered it in particular with this shortcut, but you never know...
With JAWS, the equivalent is Jaws+3, but I doubt that'll be an issue if you're using JAWS.
Normally I would say that CTRL+R doesn't work because maybe another program is taking that shortcut globally across your entire system, but space bar not working is indeed quite strange. Can you try it in Chess? It doesn't matter even if you don't know how to play it at all, just start the game, space bar will just open a dialog to type your move, you can close it with Escape.
If it works, the only item coming to my mind is that you are trying to place a flag somewhere impossible, for instance on a square you already discovered or a square which already has a yellow flag. Anyway, further discussion of that game is probably best done on the beta testers forum, but let's see if the problem can be globally resolved...