「てく」is often a contracted form of 「ていく」, so your sentence means
Okay, I am going to take attendance now.
where 「ていく」is a helping verb that tells you the action starts now in a forward looking manner.
Yes,「ている」can be used to talk about a repeated action, but this is one of the tricky grammar points where Japanese and English diverge and the nuances are hard to grasp. Since you already use 「毎日」in that sentence, you can just use the dictionary form. When you use 「ている」to talk about a repeated action you stress its continuity and the fact that it is still ...
Rather than the ～て行く or ～てくる grammar points, this is just the conjunctive て. I think it would be easier to understand if the sentence was written like this instead:
It would be better if you stuck a bell on your bag and went.
行く here is being used in a literal sense. "stick it on your bag" and "go (hiking)" are ...
After I spend more time with this question and read lots of article and watched few videos I found the answer.
So て-form has many usage, but we are only interested in the connecting fuction which has the following cases:
expressing the chronological order of actions: in this case we just connecting/linking verbs in chronological order, but no logical ...