Q: Is the GPWS inhibited below some altitude on approach (similar to the A/T below 100' RA)?
Normal GPWS modes aren't inhibited
How do you define normal? If you look at detailed notes on the GPWS system, there are inhibits. For some modes, the inhibit is 30 feet. Inhibits can vary depending on closure rates and configuration and can vary enormously (e.g. up to 1000').
There is an AIRSPEED LOW caution (or advisory) fitted to Boeings. However, these are options. I'm assuming Asiana has not opted for an AIRSPEED LOW caution (beeper and message), otherwise it wouldn't only be the Second Officer alerting the flying pilot of his speed error.