Can you take the plants outside in the summer?

damping off usually means that you need sanitation. Make sure you're using good seedstarter mix, clean pots, clean trays, clean covers. Sterilize the inside of that greenhouse too. You'll have much better results.
You need a shade cloth for summer along with your ventilation. If you're too lazy for shade cloth, there's shade paint that can be applied to the outside and they say it wears off by fall. Haven't tried it yet though, so can't say first hand.
You should be able to keep almost anything if you keep it at 50 in the winter and take the plants out in the summer though.

I do have shades on the windows, but I will admit that sometimes I just forget to pull them down in time for the big bake! Maybe I will experiment this summer by taking some plants outside and keeping some in to see how they do. Damping-off, ugh. I had several years with no damping off, then it attacked! I have sanitized, used cinnamon and chamomile, watched everything like a hawk. Obviously I must have missed something. Very odd.

switch seed starting mixes then. yours must be old or bad or something. Also try presterilizing the seeds in a 1 part bleach/10 parts water dip of bleach before planting. one thing, when you take the plants outside at first in the summer, put them into deep shade, protected from wind. Then after a week or so, put them into a little more sun gradually or you'll sunburn everything.

Depends on how much effort you're willing to put in. Peppers will survive, and fruit a lot in the fall. Certain tomatoes are more heat tolerant than others. Cacti will do well, and so will violets and daylilies. If you can handle it, bananas might work, too.

Ever since I started bottom watering, I have never had a single container develop a dampening off problem, as the tip of the container does not get wet.

But, if you are not willing to put in the time, effort and maybe expense to control temps in summer time, I can't see you being anything better than mediocre at germinating seeds. Even before I had a second layer of plastic on my GH, I was getting temps as high as 135 inside the GH if I forgot to open the door and turn the fan on. And this was in late September, early October when the ambient air was in the mid 50s to low 70s.

Mike