Hi, You're right; there is indeed an issue with the Jade and Mel quest.
As for the gym: It only opens at the end of Ava's fourth quest, after these four steps:
1. Beach, morning, any day: meet Ava
2. Beach, Monday morning:
3. Beach, the following Monday morning
4. Beach, another Monday morning.
The gym opens at that point.
I'll fix these bugs quickly and get back to you once I've released the corrected version.
Thanks for the feedback—it helps a lot.