I'm fascinated by the fact that we can set the fee. Suppose I set it to the minimum (or zero...?) is the transaction guarenteed to go through (with the delay)? Thanks.
The minimum fee you can set is 1 sat/byte.
The total fee depends on the size of your transaction, which increases with the number of inputs and outputs (so the total fee vary)
Even 1 Sat/byte transactions are guaranteed to go through, but you may have to wait a couple of days. Personally, I see no problem in waiting a few hours or even 2days (never waited more than 36hours and i always use 1sat/byte.
One additional parameter which let you control the fee is the type of address. If it is segwit your transactions are smaller so they are cheaper. I recommend you download electrum.org wallet for desktop or samurai wallet for android to get to know bitcoin a little more
Few years ago you could make 0sat /byte transactions, but not anymore.