Thanks for the answer.
I continue getting 503, or 500, or whatever after a long time waiting for the response... I was thinking that maybe is a problem related with db but it would be weird (my db is near to 250kB)
I tried to check if SSL is the reason for, but the tool from HelioHost says that the score is "Grade A"
This is what Logs shows almost everytime I guess this errors appeared after waiting browser to load (no matter if I tried to get into the website through mobile or computer). I accessed to website and then started a timer, and it loaded the error after 65 seconds...
I tried too with "mysqli" instead of "PDO"... In the beggining, seems to be faster, but day after change it, it seems the same.