Petko does use VPS.
Some prop firms will allow EA’s but some will not allow them in certain account types. Usually you can find out if they allow EA’s by reading the rules for the challenge. I do know that FTMO does allow the use of EA’s.
It is often advised if you are using a funded account that a VPS should be used. However a VPS is not necessary if you keep your MetaTrader MT4 / MT5 active 24 hours a day during the trading week. The problem occurs if there is a power outage or your internet service goes down. For this reason it is advised to use a VPS or some other form of backup so the EA’s will continue to trade.