Same question. I kind of feel lost at times about the word order. I think at some point during the course it was stated that Hungarian doesn't have a strict word order, yet the sentences like this keep insist on a rigid one. Can someone explain?

-ni is the infinitive ending (like -er in French or -are in Italian etc.).

The -e- is to make the -stn- cluster of consonants that would result from "fest + ni" easier to pronounce for Hungarians.