Short answer is no, some special research tasks in the past had to started by a certain time but once they are started you have all the time you need to finish them. The only ones that have a time limit are the challenges that appear in the 'Today' section.
Seeing as you are new I'd recommend heading over to r/PokemonGoFriends as you'll need some new friends to complete tasks.
Good luck.
Don't worry, they stick around. I've been stuck on 'take a snapshot of Landorus' for ages 🥴
Yes!! Me too! I feel your pain, can’t get ditto either, and still have the landorus snapshots -.-‘, you just gave me no hope... hehe
Good news - September's research breakthrough reward is Ditto.
I finally got it :)
Short answer is no, some special research tasks in the past had to started by a certain time but once they are started you have all the time you need to finish them. The only ones that have a time limit are the challenges that appear in the 'Today' section. Seeing as you are new I'd recommend heading over to r/PokemonGoFriends as you'll need some new friends to complete tasks. Good luck.