You can absolutely do both of those things. I book and check in with debit cards routinely, and there are major carriers that rent cars on debit cards.
There's one gotcha though with using a Debit card for car hire where you cannot access the money for the holding deposit until the hold is released. Learnt that the hard way.
With a credit card it's not money you intended to use so you don't care - unlike cash in your debit account.
Booking a hotel without a credit card requires a deposit. I've had to pay up to a $500 deposit on a hotel stay before. Yeah you get the money back after, but not everyone has that type of money laying around.
Not to mention that the deposit will not be available until 3 to 5 business days after you check out. It usually takes that long for the release to go through. (because obviously in this day and age, technology is not yet fast enough to process a transaction in mere seconds).
With a credit card it's not money you intended to use so you don't care - unlike cash in your debit account.