Should I require a security deposit or just charge a card on file?

Both work; a card-on-file with pre-authorization is more common for lower-value equipment since it avoids holding cash, while a stated deposit is more common for higher-value or specialty items where the hold amount needs to be clearly disclosed upfront.

Can I charge a late fee and a damage fee on the same rental?

Yes, as long as both are disclosed as separate line items in the rental agreement the customer signed -- combining them into one unexplained charge is what triggers chargebacks and disputes.

Damage and Late-Return Policies: How to Write Fair, Enforceable Terms

How to write a rental damage and late-return policy that actually holds up -- what to charge, how to document condition, and the language that keeps disputes out of chargebacks.