I must be overlooking something here: But how does the borked Firefox on your desktop machine affect this Amazon stick?...
Also, from looking at your log I think you meant "per minute" rather than "per second", right? That is totally fine concerning the load it imposes on your device.
During stress testing the FTL engine, we have found that the limit for a Raspberry v1 is around 50 unique queries per second. However, I'm a bit concerned that your requests are rarely answered from dnsmasq's internal cache which would come at negligible computational costs. Instead, the all ever same queries seem to be forwarded virtually always instead of being delivered from cache.