Growing your own food? Welcome to the dark side. You have a lot of learning to do :)
Yes, you will want to keep track of your greenhouse temps and for sure keep the door open on sunny days, and even days that are calm and overcast. Put a thermometer in there and you'll be surprised at how high the temps can go! One afternoon without cracking the vent can cook all your seedlings into soup.
Having said that, make sure your GH is secured so a stiff breeze doesn't carry it off. Tie it down with whatever!
Google this group for seed starting advice - lots of folks have been down the road you are just starting on. There will be conflicting advice but if you are truly concerned then don't put all your seeds into one method, try a couple on for size and see what works for you.
You will not need to feed seedlings until after they develop their true leaves. Seeds contain all the nutrition they need esp. at first! True leaf-stage is when you can think about potting on your seedlings to larger containers. I fertilize with a WEAK mix at this stage, give them a day in the dark to recover, then feed again when planting out. Some plants want a side dressing when they begin to bloom.
Sprays come out when I can't stand the pests anymore - but that's indiscriminate, and likely to hurt the good bugs as well as the bad bugs. A better choice IMO is exclusion - if you have a crop that bugs love, put some floating row cover over it and say goodbye to re- applying every time you water or it rains.
The plants you have seeded in the garden don't get moved. Some plants will over-winter for you: in Z5, that means onions, spinach, garlic. First crops of the season are from over-wintered plants for me.
Good luck - do more research! As Mulder might say, the Truth is out there - waiting for you!