Email Deliverability - Recipients vs. Sends and Suppression Lists

Hello, there is some concern with the deliverability rate of our emails. It looks like our Deliverability rate is consistently above 98-99%. However, the total recipient list is always much higher and we are seeing a "sent" percentage of only about 50% and "rejected" percentage of about 40% typically.

When looking at the rejected recipients, it looks like it's largely due to "already undeliverable" or "already unsubscribed". My guess is that, because I usually compile the send lists from reports, it shows everyone who meets the criteria that I would want to send to - but doesn't actually attempt to send to those people who are already undeliverable and already unsubscribed.

Is this understanding correct or are there any additional insights to help me better understand? I think the high "rejected" rate is tripping my team up. 

Also, I do have a suppression list for unsubscribes. When putting this list in the "exclude" area, will these people still show up in the "rejected" area? 

Is there a suppression list I can set up for undeliverables? If so, I have the same question as above - if that suppression list is excluded, will they still show up in the rejected?

Thanks!