Anyway for the other two colour illustrations:
Using will/would isnt wrong. But using "will/would" here would sound like she's asking for a request to him."Do you want to come with me?"
Just that one phrase.
Ren wasn't able to comprehend that one phrase right away.
So using "Do" here would be appropriate since she's giving Ren a choice.
Yeah. Even the direct TL would be "guts", it doesnt sound appropriate in this context. So using "You've got some nerve" is definitely better here."......You've got some nerve.
Peeping on my body, are you?"