Yahari is like "I knew it" or something. and Kamoshirenai is like a "possibly" at the end of a sentence. It might not be so but it might also be so. It's sometimes shortened in colloquial speech as "kamo". Yahari seems to change exact meaning depending on the context. https://www.japanesewithanime.com/2017/01/yahari-yappari-meaning.html https://nihongoshark.com/kamoshirenai/

I have never heard this phrase either, Tuesday week? ??? Hmmm usually it's just this Tuesday, or next Tuesday here in the states.

When I say 'sect' I definitely pronounce the t. It's still there in the plural but the 's' slurs it.

It depends on how well read you are. I don't think people really read as much as they used to so a lot of older words that mean specific things are dropping out of use. I would definitely use 'ordeal' in casual or formal speech, and I like the way 'tribulation' looks up there too. You can also say 'trials and tribulations' to refer to an ordeal(s) if you want to be dramatic. 'She had to work hard through her trials and tribulations to get where she's at.' 'This is a disaster!' or 'What a nightmare!' are also things people say, usually when they are being a little dramatic :)