Can he enter from any European country if this is the first time he enters to Schengen in case he has a connection ticket to show in the first border?
The scenario you described in a comment, namely entering through another country to catch a plane to your final destination (the country that you said you were visiting and that issued your visa) is absolutely no problem. Changing plans, not having a ticket, etc. are not necessarily dealbreakers but might raise questions. Earlier questions on this site detail when that can cause problems but, if he is only transiting in Amsterdam on the way to Poland, there is no need to worry about your father's trip, that's exactly how Schengen visa are designed to work.
He got his three vaccination but unfortunately the vaccine they did seems that not acceptable in Europe (Sinofarm) I am not sure. Anyhow if we want to travel to other countries what are the conditions now? If we use Blabla bus or Flixbus does any check for that?
I cannot report how frequently they check in practice (and we don't want to advocate breaking the rules on this site) but some form of certificate is required and the driver is supposed to check. Fortunately for your father, he may still be able to take the bus:
- France is lifting all requirements (except wearing a mask) effective next Monday.
- A vaccine is not required in Germany, you can use a recent negative test instead (the so-called “3G” rule). It also seems likely that these restrictions may be lifted on March 20. Wearing a mask is mandatory here too.
For international routes, bus operators recommend checking what the rules are for your specific route (either on their webiste, on reopen.eu, or on the national website), a test might be needed.
Rules for international air transport and entering the EU from a third country in either Amsterdam or Poland are different, you will have to check what they are as well.