Quote from: Do-DMT on Today at 02:07:09 PM

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?

Yes. Miners can choose to not include it. There can be a whole lot of factors as to why miners would not want to include it; non-standard transactions, fees are too low, miner's preference, etc. No one can really tell you the odds of it happening; generally miners do not actively exclude specific transactions and non-standard transactions should not happen if your wallet is functional. I vaguely recall there's one mining pool that mines non-segwit transactions exclusively.

Quote from: Do-DMT on Today at 02:07:09 PM

If there's a re-org and the transaction goes back into the mem-pool, would it be confirmed automatically later?

Depends. See above, it'll only be confirmed if it's included in the block in the longest chain.

Quote from: Do-DMT on Today at 02:07:09 PM

Also, what was the longest period of time you had to wait for a confirmation?

Weeks.

Quote from: Do-DMT on Today at 02:07:09 PM

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.

Possible. How much fees did you pay? The minimum fees for a good propagation is 1sat/vbyte and can increase depending on the mempool capacity (which I assume isn't the case). Poor propagation is not all that common anymore, what wallet are you using?