uçuverdi is a conjugation of uçmak (to fly). It expresses either surprise and unexpentency or the action being smooth and easy.

uçuverdi :
1. has just flown away
2. flew away

Smillarly we say gidiverdim, geliverdiler, bakıverdi, alıverdik, oluverdi etc.

Kitap elimden düşeyazdı
Öylece bakakaldı
Kuş elerimden uçuverdi

What is the name of the verbs like these?

'düşeyazmak' is a word one of our frieds thought was funny to mention in a language web site. The reason why it was funny is that such a word doesn't exist in standart Turkish.
Now our problem is that from time to time learners still mention this word and everytime we have to explain them that this word is non-existent in standart Turkish. In some cases our funny friend turns up and supports his argument by mentioning that this word is used in some city in Turkia. I agree that it is a local thing but this doesn't mean it is part or standart Turkish. Most native Turks, even the ones with higher education or even most Turkish teachers don't understand that word. It is best to avoid it.
Do you think it was funny to mention a non-existent word in a language forum? Sometimes I forget about that word and then one day suddenly it appears again from nowhere and I remember the meaningless discussion with our funny friend.
These are the kind of things that make people crazy and end up in an hospital, aren't they?

No it's a local thing my friend. The problem rises when people think it is alright to use local words in written language. But of course it is not a good idea. In every language there are local words and you are supposed to use them locally only.
Most Turks don't understand that word. I don't bother looking to a dictionary either.

gelebilmek

gelmek ve bilmek

this is also such verbs

So what does that mean?   gelmek = to come + bilmek = to know but surely ´gelebilmek´ means ´to be able to come?  What does ´knowing´ have to do with it??