Hi, welcome to worm farming. I've been doing it for about a year now. Questions are good, and lead to learning more. Hope we can help out.

1. They like it best at 70, but thats not to say you can't keep them in a place that is hotter or colder. I have a bin outside, were it is 100+ during the summer and as low as 0 during the winter, and it is very active.
2. Thats a big bin. How many worms do you have? I would worry about how much air they get if you have the doors on. You would want it covered, but the fridge is made to hold air in, so if you keep the lid on, give it plenty of holes for fresh air flow.
3. Grass clippings are fine, but they can heat up. I would use in moderation. I will bag mine up every now and then, and use in my regular compost pile. Leaves, newspaper, veggie scraps make up most of my worms food and bedding.
4. As stated with the grass clippings, they heat up, so your worms could be escaping the heat. when things cool off they may find their way back.

Don't let any mistakes now make you think twice about what you are trying to do. This is a great thing to do, you'll make mistakes and learn from them. Once you get it down, it is easy. You just have to learn what works best for you.