What meaning does the prefix やって give to the main verbs? Is it a constant one can do with some other verbs as well? For example やって来る やって見る やって退ける やって行く
やって is basically just the te-form of the verb やる, which has various meanings. As @Leebo points out, most expressions in the form
やって + another verb can be understood using the ordinary grammar of subsidiary verbs such as (て)みる or (て)くる.
- やってみる: to try doing (it). See: What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"?
- やっていく: to do something and go; to do something before leaving. See: Difference between -ていく and -てくる
I'll leave home after finishing my homework.
- やってくる: to have been doing something over time; to keep doing something up until now; to do something before coming. See: Difference between -ていく and -てくる
I have been doing this job for 3 years.
...and so on and on. In the examples above, やって means just "to do".
However, there are a few verbs that have (additional) fixed meanings:
- やってくる: to come along; to come all the way
Santa Claus is coming to town.
- やってのける: to succeed in (a difficult thing)
- やっていく: to make a living; to make ends meet
These やって are still loosely related to the original meaning of やる; for example, I think やって in やってくる originally means "to bring/send". But it's probably best to memorize these as special cases. Aside from them, you can use the standard grammar to make sense of the phrase.