Question

Do you think we inherit and become part of collective bad karma, and suffer consequences of it?

Answer 1

Long time ago some boys were playing together and saw a monitor lizard go into a hole in the ground. They blocked the entrance for fun thinking that they will remove it before they go back home. But they forgot to do so and the monitor lizard was trapped inside the hole. After a week or so, they remembered about the monitor lizard and came and cleared the blocked entrance. The lizard came out looking very weak. Then they gave it food and revived it.

These same boys were born during the time of the Buddha after many a lifetime. They became monks and were travelling together. One day they had to take residence in a cave. Due to overnight heavy rain, a huge stone collapsed and blocked the entrance. They were stuck in that cave for 1 week. This was a consequence of the bad Karma they had done together in the past.
 
So to answer your question, you do not have to face the Vipaaka(consequences) of someone else's Karma, but if you commit similar Karma as a group, there is a high chance that you will be together with the same people when you reap the consequences.

Answer 2

yes, definitely true. Our life is reflection of our mind, our mind continuously creating karma, keeping us trapped in Samsara. Drop the defilements of the mind, stop -ve karma, exit the trechary, exit samsara, nibbana.