であり is the continuative form of である (a literary and stiff copula), so it's used to connect verbs in a broad sense. However, you have missed ながら, which in this context means "albeit/despite/although". 当事者でありながら means "although she is a person involved (in the matter)".
What is the difference between ながら and のに for expressing "despite&...
'昨日私のおじさんをてつだいました' is the correct one.
Xをてつだいました when X is the object of 'help'
'にてつだいました' is possible as a sequence in other cases. See https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q10135898565
Also as a side note, '昨日おじさんをてつだいました' would be more usual (without '私の') if the helper is 'I'.
I don't have very grammatical explanations, but let's focus on the second sentence.
Suppose he arrived 10 July 2020. Today it is 10 July 2021.
Then '彼がここへ来てから一年が経つ' can be used yesterday (09 July) or today or tomorrow (11 July). Or in past (say a week ago) or in future (a week later).
'..経った/経っている' on the other hand can be used today or after, not yesterday. ...
I found several people who think らぐ is some kind of suffix, but looks like this is not explicitly listed in dictionaries as a standalone suffix. If らぐ is a suffix, it should be similar in purpose to English -ate used to turn words into verbs (e.g., formulate, activate).
My major is not linguistics but I found some interesting references for you.
Aoki introduces a few types of classification of transitive/intransitive verbs in Japanese.
The first classification is written by Kuginuki. It says there are 3 patterns of transitive/intransitive verb pairs.
Depending on the type of conjugation (第Ⅰ群形式)
知る (四段活用 is an ...
You can stick to 歩いていく in most cases (according to my reflection for a few minutes). At least, I don't think there are cases where using 歩いていく instead of 歩く can be a source of major confusion.
駅に歩いていく means I walk to the station; 駅に歩く is not really grammatical.
駅まで歩いた means I walked up to the station. This implies 'I reached the station'; ...