I wouldn't drop the frequency from every 3 hours to every 7 hours;
maybe start by taking her out at 1 for a few days, then at 1:30, etc.

How long dogs can "hold it" varies greatly;
you'll just have to learn what you can expect from her.

don't know the timing of vaccines;
it's been too many years since I've had a puppy.

Maybe Meghane will pop in pretty soon.

One of my oldest friends has had Bassetts as long as I've known her (we met at a Rolling Stones concert in 1965; she tells people she wasn't really a teen-ager, she was a very precocious 5-year-old!), & she would agree;
hounds are indeed stubborn!

but Annabelle looks like a Lab mix, & they're eager-to-please as well as smart;
I think you'll be delighted with how she learns.

A general rule of thumb is that a dog can hold it 1 hour each month of age up until 6 months old. After that, you should be able to expect an all day hold.

However, consider what you would do. I can hold it all day myself but I don't find it comfortable.

As far as the shots are concerned, your vet will be able to help you there. If you don't have a vet, your local animal shelter should be able to help you. It used to be that spaying was done at 6 months, but I think it is being done earlier than that now.

Distemper/parvo vaccines are every 3 weeks until puppy is 18 weeks old. Your vet will know which other vaccines are needed in your area (lepto, parainfluenza, bordetella, hepatitis, etc). Rabies vaccine requirements vary by state; obviously your vet will know the law. Heartworm prevention starts at 6 weeks. Deworming is every 2-3 weeks for at least 2 rounds. Physical exam is important at 6-8 weeks and at least again at last vaccines to make sure there are no congenital defects etc. Spay is before first heat cycle to prevent breast cancer later in life. For most hounds, that means spay at 4-6 months.