Can I break bread at a person’s home if I’m aware that he has a haram income and what to do if they invite me to their home and ask to have dinner with them?

Yes it’s permissible unless you know that the food being offered to you is itself haram (meaning it’s stolen, or it was bought with money that was specifically haram). Now usually these days that’s not the case. We buy the food for a general amount of money (like $10) then we pay. This would be ok. But let’s say I have haram money in my hand and I tell the store owner I buy this bread with this specific money in my hand. If this is how the transaction is done then it would not be valid you should not eat such food. But honestly this is rare.

So generally yes you can eat there.