Incoming mail is very doable.
Outgoing mail is hard because no one will your trust your server, the easy way is let someone else send your mail.
People get stressed about your receiving server being down sometimes, but this actually not a big deal. Mail senders typically will try for 48 hours or so to deliver mail, and if it doesn’t get delivered it will be sent back to the sender with a “could not be delivered” message. Very little gets actually lost.
I don’t use Whoogle myself, but I’ve checked the code and seems like Whoogle indeed uses HTTPS when sending your query to Google.
(And as long as you are on your own private network at home you should be fine using HTTP)