It is a "display of confidence", meaning "submit myself to something unpleasant if I prove to be wrong" as in:
If the train arrives on time, I'll eat my hat.
To say "afterwards I had to eat my hat" is to admit that you were wrong.
http://www.phrases.org.uk/meanings/eat-my-hat.html
"Keep up the good work" is a nice expression, but because it's phrased as an imperative, it's one that can have unintended nuance.
One common use of this phrase is of a superior complimenting and encouraging an inferior in the workplace. For example, suppose your boss asks you to do a project, and you show her some preliminary results. She might respond:
This is what I'm looking for. Keep up the good work!
to indicate approval, but also to tell you that the project is not complete and that you should keep working on it. It comes across as kind of an order.
I agree that if someone is doing a favor for you, it can be an odd expression. It may sound like you're asserting authority over them, when they would rather feel like your relationship is as equals (or even that you owe them).
The exception is when someone is working on something that does not relate to your own benefit. For example, suppose a friend is doing a good job on a report for school. You might say:
Looks like you're almost done. Keep up the good work!
as a way to encourage her to complete the report. In this case it's more like similar expressions such as "Don't give up!" or "Hang in there!", which, while phrased as imperatives, are not interpreted as orders.
Best Answer
"like for like" is a short way of saying "if you click 'like' on something I post on Facebook, then I will click 'like' on something you have posted." It is implied that one or both people involved will not care about the posts that are being "liked," and that they are only doing it to increase their total number of "likes" any way they can to seem more popular and important.
"follow for follow" is the same thing as above, but for Facebook's "follow" feature instead of its "like" feature.
This kind of thing is usually considered anywhere from annoying to harmful, so many places do not allow it.