@omk3 you both typoed the volitional here (can’t remember if the last time was also this club). It’s 入ろうかと
The bag thing you see in the picture she has under her arm with the seashell keyholder. If you google pictures with it you will see many variatons of it. Seems to be a pretty new word since like omk3 says the most dictionarys don’t have it. search
@omk3 already has a nice explanation. XといえばX is surprisingly common. Here is something from one of the pervious discussions of this construct Can't figure out how to think about this sentence from 窓から逃げた１００歳老人 - #11 by Leebo
Point 2 of the linked thesaurus gives a (japanese) explanation.
To me it’s part of the whole sentence it connects with the previous sentence. She is thinking/lamenting wich club she should join but while she is idlying her time away/not making progress towards joining any two weeks pass and she misses joining any and stays that way (まま).
EDIT: ah I didn’t register that you thought うちに could mean at home. See @sumsum answer 2 posts below for a better explanation.