If I purchase bitcoins via p2p, can I get some problems if the bitcoins I get were involved in some criminal activity ? If yes then how do I avoid such situation ?
Not that much mate , because unless your country has an issue about Bitcoin transacting then you will face with that problem but not in the sense of when the transaction is legit.
and like what the first answer says? just explain that it comes from p2p for safer explanation .
or Use Mixing service if you think there will be something to face when you start transferring the Bitcoin .