Is this normal? I am having terrible problems with my DB lately (very slow and inconsistent) and some users are not even able to post at all.
I would like to do any housekeeping that might possibly fix my slow DB at this time. Any suggestions?
Unable to communicate with Simple Press server
that wont affect speed of the plugin itself… but the fact your server cannot communicate with the simple press server could indicate a server issue on your end… we have tens of thousands doing it regularly so our server is operation (as you posted here too)…
what sp version are you on?
Version 5.4.1
I think you are right. The host never admitted to any trouble at first but had an emergency relocation of multiple servers so I opted to move it. Now on a more powerful cloud VPS which seems to be way faster. My site was alone on a dedicated private server before that but with a less powerful processor. Of course that should not have been a problem but multiple servers including mine were down the day before my move, which was last evening btw. 
After the move, is there any type of housekeeping that you recommend? SP is very fast now.
That is good news.
As to housekeeping then I would think just the usual although I do like to to recommend regular optimisation runs on your database.
Check the SP profile form. If there is any issue it may be because the root path has changed a bit and you will need to reset the profile tabs and menus in the forum admin > Toolbox > Housekeeping panel.
And I hope all remains well for the future.