So, after like four days of having interruptions to my domains, I am finally experiencing no more trouble. None of those wordpress errors anymore. I hope it remains like this for a long time to come.
And how do I solve the problems? By paying for more RAM and getting the server all for myself. So, as usual, money is the culprit in settling problems, isn't it? No amount of technical knowledge can help. My webmaster disabled the Cron jobs (whatever that is), I deactivate several plugins and voila, no more server not available problems.
I am going to keep my fingers crossed and hope nothing bad happens again. Anyway, in restropect, I think it is high time I upgraded to my own server because of the domains I am running now. So, it is money worth spending. This also means I must work harder now.