I have spoken with a specialist in regards to both aspects of your question and have even spoken with a couple of private grant writers that have experience in the realm of finding and applying for grants for profit businesses.
Here are the results I came up with:
1. Small business grants are FAR and few between. If you even qualify for one, it would have to be in a redevelopment area, like the Ward 5 area here in Las Vegas, NV.
Even then, you would have to be a business that is under certain conditions financially. Most times, when business grants are farmed out they get whittled down to the state, county and city levels. Once they have been, they usually turn into business loans. SBA has their list of approved lenders and you can get that list from your local office.
2. Don't worry too much about what program is good for your business. Try this first: Go back to the franchisor and ask them who they are already dealing with, if anyone. they should have some kind of agreement with someone already that has SBA lending approval, or a lending institution that may have connections to the SBA.
If not, contact your local SBA and they can help you find an approved lender that will be able to help you figure out the right program for your type of business. Also, be sure you are a franchisee not a licensee like 7-eleven does. You are afforded a lot more as an actual franchisee rather than a licensee.
It's not that small business grants do not exist, it's that they are extremely hard to find, and you're better off working with the SBA and letting them help you find the right program for you. The SBA is available and will try to help as best they can. Once you do find your lender, make sure you follow the blue print from your franchisor--they didn't get successful by throwing a bunch of ideas at the wall to see what sticks. Their business plan is meant for you to succeed.
Keep it rollin!