Sorry, but I respectfully disagree with IAAL on this one..... there are cases where a landlord can evict over them.
If the landlords lease agreement (the one you signed) specifically notes that late fees are applied first to any payments, then the issue is no longer overdue late fees, but under-paid rent. And the landlord can evict if you do not pay the full rent when due.
Further, most leases (at least the ones I am familiar with) have a statement that late fees are 'liquidated damages' and therefore could also be valid for eviction.
The key here is how the fees are shown in the lease..... and your acceptance of them by your signature.
"Can they charge late fees on top of late fees?"
*** Yes. However, the example you provided ($50 the first day, then $10 per day after) isn't really 'late fees on late fees'. It is simply a 'continuing penalty' and that is not improper.