They can as long as they get enough light and have plenty of room. Zucchini can get very very large as can tomatoes- especially indeterminate varieties.

If you do have the zucchini inside, you will have to hand pollinate or the plants will not produce anything at all.

You will need to shake the tomato flowers in order to make sure they get pollinated properly. This mimics the effect of wind blowing them as well as insects crawling around on them.

She was wondering if the plants will grow in her enclosed "sun room" for protection from animals.

I assume she is using pots/containers? For tomatoes I recommend a cherry type, the regular sizes can easily get blossom end rot (in my experience anyways). It could just be me but growing veggies in containers is a futile effort, particularly for production and quality. The squash may turn out bitter if growing conditions aren't right. Sorry to be a negative nelly, your daughter could have a much greener indoor thumb than I. If she could fence in her garden plot with some deer deterrents that may work out better? Best wishes!

Agree with vgkg. There simply is no comparison possible between indoor and outdoor gardening results. So many factors are involved that indoor gardening starts out with 2 1/2 strikes against it and only for those who have no other options at all.

Deer are a common gardener problem but they can be controlled for.

Dave