Answering your questions in:
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I am waiting for detailed description and screens from my client.
About the 3 questions you asked:
2. smartphone app will not need Login, but login will be required for admin sections.
3. When user selects the offer and coupon, a mail will be sent to the respective fitness center and a counter will be added which will display in admin section indicating the number of users who opted for the offer.
I am waiting for the design and final description from my client. Will write back after hearing from them.
Let me know and please don't accept now.