Does the october's field research reset on november?

No

No. Once you have a research task in your list, it's there until you either complete it or delete it. I would recommend having a space open to still complete a daily research task regardless of how good the weekly breakthroughs are, but you know your biome and how long it will take you to complete 10 water evolves

Like said, they won't disappear, but I would recommend you to complete them as fast as possible or ditch one. One dratini is not worth skipping several days worth of daily stamps.

Better get them done before the 2x candy ends.
Sometimes I like to leave one behind to chain together the "catch a dragon" task.