After reading the latest links you've provided, and ingesting other comments, I have these thoughts:
- at best, your connection is unencrypted and 1MB (about 3G speed) per the FAQ
- Netgear wireless extender is designed for use with other Netgear routers. you get results, but the spotty behavior and such may or may not get better
- the extender halves the throughput
- muni techs have a range of ability and knowledge. you may find other techs, or users, who have better solutions to maximize the free public wifi. keep in mind it is 3G at best
- sounds like the network got saturated real fast, and you are seeing effect of that which is time-based
- make sure you've entered a password for access to your extender wireless. read the user manual and go to the web interface of the extender. you want to determine if others are connected to your extender. after skimming the user manual I think that is possible, but you've probably done this.