Nightly mushrooms grow at night, not 5 am. My sim lives in the Bramblewood, so I'm not sure what time they do grow, but she managed to harvest some just before I quit playing last night, and I want to say it was around midnight? Also if you have seasons, they're a winter plant.
Bird/bunny help with crops I'm still working on, but it does seem they'll prioritze oversized crops over regular ones.
The plants dying I think is a known bug...
I think this is the right AHQ thread
https://answers.ea.com/t5/Bug-Reports/OPEN-Plants-always-die-before-even-blooming/m-p/10283837#M180753
