Is Jackass's Research even possible right now?

It's technically possible to do these quests where you are now, but it's much easier to do later, as the enemies do not scale with you; they have a set level. Personally, I wasn't able to do the final part of this quest until I went back.

Once you've unlocked ending C or D, you will also get access to the Chapter Select menu. Since your level carries over across routes, you can come back to do this quest as a level 99 2B, which will make it trivially easy to complete.

However, it's worth noting that this quest is a 2B-only quest, so if you don't do it now, you will have to wait until you get Chapter Select to attempt it again.