Yes if there is damage, you have to pay & then recover from your insurer. If you know that & budget for it, you avoid very expensive insurance from the Car Hire Co.
No, the Car Hire Co does not charge the deposit to your card, at least the Co I use does not.
What they do is "Pre-Authorise" the deposit, i.e. check that your card is good for the deposit amount. This does not appear on my card statement & I have never been charged interest.
Of course it depend on which Car Hire Co you use, and the quality of your credit card provider