Someone gave me three separate cheques, each written with a different pen, and they all bounced. Will this affect my chances of getting my money back? How likely am I to recover what’s owed to me?

The fact that the cheques were written with different pens is irrelevant under Indian law. The key factor is that they bounced, which constitutes a legal default. Your chances of recovering the money depend on the specific circumstances, but you have legal grounds to pursue the matter and can file a legal case against the issuer.