Hi guys (and gals? )

So here's what I'm Wondering;
After a transaction is made, is there any chance it won't be confirmed at all? If so, what would cause it not to be and what are the odds of that?
If there's a re-org and the transaction goes back into the mem-pool, would it be confirmed automatically later?

Also, what was the longest period of time you had to wait for a confirmation?
I once made a transaction that took almost a day for it to be confirmed, and if I remember right it also took a long time until it even appeared in the recipient's wallet. could it have been the result of a bad wallet? It was about a year ago so I don't think the network was very busy.

Thanks!