Does it make sense to use full recovery if the data and log files are on the same HD?
I can't speak to 1 but for 2, I don't know that your position should be pushing the business toward a specific RPO (recovery point objective). They may not be aware that they'd have to re-enter all the data for a day if things go belly up. Talk to them, find out how much data loss they're willing to tolerate. If they say 24 hours is too much, great, then that indicates the current approach is insufficient for their needs. If that requires hardware purchase to meet the RPO, then they will need to provide funding or accept their current max data loss. Finally, document the outcome in some public place and then test on your restores a recurring basis to ensure you are able to meet that RPO.

That said, there are plenty of other reasons to have data and log (and temp) on separate drives. Some of them documented on this question https://serverfault.com/questions/38511/ms-sql-layout-for-best-performance