I'll be able to complete it in less than 24 hours myself but it's probably going to be a Moltres again. Datamines show code in the research tasks referencing the month and the research is still fire-themed like when it started. The best theory is that we'll get a new theme for the research in May as well as a new breakthrough encounter.
How many days until we find out what the next research breakthrough is?
I'm one day behind on the stamps, got 2 more left, so I guess tomorrow evening when Japan completes it or when? I'm curious to know what the next pokemon will be.
Answers
Research reward pokemon do not run. And, in fact, you can run and return to the reward later.
Some people have been intentionally holding onto their Moltres or other rewards with low base catch rate like Typhlosion to use as targets for quests like "three great throws in a row". You can still collect daily stamps while Moltres is waiting. The main issue is that you can't see whether you have collected a daily stamp today and can't see how many daily stamps you have while the reward button is blocking the stamps.
We'll probably find out in just a few hours. Some people change the time zone on their phone to get the reward earlier. I'm 14 h away of getting my next with no tricks.
Yes, probably moltres again. There are two main theories:
1- It's a monthly featured pokemon
2- It's a number of field research breakthroughs that grant the same reward, independently of the date you finish them.
I lean more towards number 1, but who knows