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 ?
I do not think so- criminal activity may only be linked when you purchase goods on the internet or under the dark web; and bitcoin is decentralized. This means that all of the transactions that you made cannot be linked or traced on the origin of their existence.
Even if the BTCs you are holding were linked to some criminal activity, I doubt that the government would absolutely characterized it that the current HODLer is the one perpetrating the crime. This is a good question and I have yet to encounter a person or some news that reported such issue.