use of the に in 一番に, and about て form Hi can someone help me to figure out what that in is doing? I´m confused. is it indicating an absolute time, or is it making it an adverbial for what comes next? and also, all the forms is the connective -and-? >

This is an adverb that means "first(ly)". is a particle that makes the **previous** word adverbial. For example means "eternity" and means "eternally". means "energy/spirit" and means "energetically". Likewise, means "number one" or "the first/top", and is its adverbial version.

Those te-forms are just connecting several actions, namely , , and ().

*
He arrived first. / He was the first to arrive.
*
The first thing my family do in the morning is gather in the courtyard and do tai chi together.