ついたちかん vs いちにち

Hi! So I'm doing lesson 13 in Genki 2. This grammar point that I'm going over is about the frequency of one's actions.

一週間に一回買い物をします etc.

I have several questions about this:

1. They use the expression いちにちに二回食べます for "twice a day."
Earlier I've learnt that to express duration of time you just add 間 to the days of the month counter:

ふつかかん、いつかかん、ここのかかん、じゅういちに ちかん etc.

Why is the textbook using いちにちに instead of ついたちかんに ? Are they the same?

2. I've see the use of いちねんに一回旅行します, should't it be いちねんかんに一回旅行します?

3. Is there are difference between 一生に一度 and 一生に一回 ?

ありがとうございます！

1) 2)
ついたち only refers to the first day of a month. You can't say ついたちかん.
間 is a suffix for a time span. ふつかかんに一回 is not incorrect, but it's more likely used for "once in a specific two days". When expressing a habitual action, いちにち / ふつか / いつかに一回 is more common.

3)
Basically the same. I think 一生に一度 is more common (as a collocation).