Where can I find these last minute deals or maybe a week or a few days before the flight?
Do these deals also exist for other modes of transport? how do I find those?
Seek out a recommended Travel Agent.
They have access to everything.
I know some (many? most? all?) airlines will send email or app alerts for great deals on near-term travel. I used to get them for both JetBlue and Southwest, though I stopped a while ago because I never used them. But check the sites of all the airlines that service your preferred airport. Less likely to get deals on international travel, I think, though you might get say off-season deals to the Caribbean or something.
Next Departure, there’s an app. Give it a try, you’ll be pleased!
Since the OP is looking for advice, let’s move this to IMHO.
Colibri
General Questions Moderator
Or Google does it too: https://www.google.com/flights#flt=/m/0qzgc..2019-05-14*./m/0qzgc.2019-05-18;c:USD;e:1;ls:1w;sd:1;t:e
Type in your starting airport, choose a starting date (or a flexible duration) and it’ll show you cheap destinations all over the world.
www.cheaptickets.com and www.cheapoair.com both work pretty well.