Am I allowed to open a Chase Ink CC for the sign up bonus, if it's marketed as a business card and I'm using it for personal stuff?

Officially not, but people do it quite regularly and all the cc companies are well aware without issue

https://www.dansdeals.com/credit-cards/chase-cards/awesome-earn-record-high-90000-points-excellent-no-annual-fee-ink-business-unlimited-credit-card/#:~:text=This%20is%20a,Identification%20Number%20field.

“Sole proprietor” is the category for that.

From the ease they allow it - yes