My full time job is advising business owners on selling their businesses. Here's my take on your OP:
There are two ways to buy a business - buying the shares (which includes taking on all the debts and potential future liabilities) and buying just the assets.
If the business is a sole trader or partnership, as seems to be the case here, your choice is limited to buying the assets.
This is a simpler route, but it's still worth getting some advice from a solicitor experienced in these transactions. I doubt you'll be able to "continue the contract". If she's in leased premises the lease agreement may not allow for what's called assignment i.e. she can't transfer her "tenancy" to you. You'll have to sign a new lease with the landlord. Bear in mind the landlord may not be willing to lease you the property, may want to run credit checks etc., on you and may insist on new terms.
Re: goodwill. I would pay for goodwill in a heartbeat if I was getting a good deal. The problem with goodwill is that, unlike with stock, you can't get external financing to cover that part of the purchase price - banks won't lend against it.
If goodwill is footfall based on location, you'll get that in any case if the landlord agrees to lease the property to you; you don't need to pay the seller for it. If there's a different component to the goodwill e.g. the name of the business, it may be worth negotiating. Tip: Ask for seller financing to the full extent of any goodwill you agree i.e. you agree the amount on paper but it's financed via a seller's note (a loan from the seller). If you're setting up a limited company to make the purchase, accept the loan in the company name rather than your personal name.
From a different perspective, exclusivity is a problem. A seller needs to have multiple buyers to be in a good bargaining position. Exclusivity with one buyer is dangerous in many ways, not just price. It can drag the deal out quite considerably during which time there's always the risk of some adverse material change. If you're the only buyer on this seller's horizon you're in a very strong bargaining position. But don't be complacent - it's not always that sellers disclose they're speaking with mulitple parties
If I can help with any other questions feel free to post below.