Hello ResideSin thank you for your reports!
Daycare updates 1x per day (24h) also your Pokémon can level up as long as its total level (including levels gained in the daycare) is below 100. The way it works is that your Pokémon can earn up to 15 additional levels while staying in the daycare. Pokémon's level by 0 or 1 randomly each time it’s checked (24h)
Eggs: if you leave two Pokémon, there's a chance they will produce an egg. However, there are a few things to keep in mind:
- The two Pokémon must be compatible—either the same species or one of them has to be Ditto.
- There's also a small chance that if both Pokémon are shiny, the egg could be shiny too!
- You need to be a VIP user for the egg to remain safe in the daycare. If your vip membership expires while the egg is still in the daycare, unfortunately, it will be lost.
Gym Battle (items) Update: Thank you for reporting the issue . We appreciate your feedback and want to assure you that we are actively working on a solution. The fix will be included in the next patch, and battles will be back to normal as soon as possible. (Edit: Fixed on v0.97c)