The answer has to do with something specific versus something conceptual. For example, "I am at work" "I am at the office." If I say, "I am at the office", then I am telling you where I am located. If I say, "I am at work", then I am telling you what I am doing. A real professor can explain it better than me, but I hope that this helps!

Oooh, this is a tough question. I don't know, if there are any rules that dictate this. I think this may just be one of those things, where it is just the way people talk. Normally, we use the definite article "the" when we are talking about a specific noun. So, like your example, a specific restaurant or store. They are specific locations to be at. However, there is a small difference with church and school, that may have influenced why people say "They go to church. " rather than "the church". Church and school are social/cultural/religious institutions. So, culturally they are more than just places to go, they are almost concepts in and of themselves. Or it may just be a dialect thing. For example, in America we say " We are going to the hospital. " But, some people in Britain say, "We are going to hospital. " I am curious, what others will think.