Ok let's go through these questions on by one below:
My company is a bar/club, with only 4 out of 13 locations serving food. Would you mark this up as a local business or a restaurant?
I would mark the locations that have food as restaurants and the ones that do not as local business. I would set up and write a unique description for each location.
It asks for "URL" above the ratings. Is this supposed to be the URL that ratings are on like Yelp or something? Or is it the URL for the page? Either way, neither of those URLs are on the page so I can't select them. If it is for Yelp should I link to it?
You can either link to your off site reviews sites by getting an embed code or you can write some code with structured mark up to embed reviews into your web site that will be indexed by the search engines. There are references on line about how to do this.
How do I add reviews? Do they have to be on the page?
Look at answer above. As a sidenote you should make it a mission to get 10 reviews on Yelp, Google, and Bing for each location as this helps your local results.
If I make a group of days for Day of the Week for Opening hours, such as Mon-Thu, will that work out?
Yes
I have events on this page. However, when I tried to do the markup for just the event it told me to use itemscope itemtype="http://schema.org/Event" on the body tag of the page. That is just a small part of the page, I'm not sure why I would put the event tag on the whole body?
Can't help you on this one.