To answer your questions...
When you reach the mew shrine make sure to walk up to it and save in front of it.
You found the hologram switch in victory road, now you need to find where the hologram was.
Dialga will be located in a rift somewhere during the soaring section and Giratina has...
You need the fourth stone which is located in a cave to the lower left of the forest. Once you have the fourth stone you'll be able to fly to the hidden area. Just a heads up though, there's not an extensive post-game. Just a few events to wrap up the story with.
I don't know if you can. This game was made for PC. Any other platform is going to require an emulation. For mobile it's Joiplay. You could try WineBottler.
Other than that you'll have to find someone who knows Mac emulation.
The scientist detect something was going on over in west stronym. You need to navigate that way.
If you get stuck you can always watch a playthrough of the game over on youtube. I recommend XatumiKO.
Prof. Pines tells you to head to the Klonen Building (the one with the latias & latios statue). In there you'll fine some scientists who will tell you where to go next.
You need to find the 3rd anomaly. It is located in the room with 3 yellow lines on the floor. You need to run over the lines until the rooms change. You'll know the room has changes when the game lags for a split second while crossing a line. You need to find 2 switches in this room. Afterwards...
Are you in the Lecture Hall currently? At some points in the game, not frequently though, the save feature is disabled. That being said when you press the X key there should be an option called "Save".
There is one final solution for this problem and that is to send me your save file. I have have it fixed in a few minutes. If you need assistance accessing your save file I can PM you instructions on how to access and the file.
100% it will require the patch.
To apply the patch simply drag and drop all patch files into the game folder. The important file is the Void.rgassd which will be replaced with the new one.
After you have applied the patch:
To unbeach your swampert you will need to black out. I recommend...
No, but I am working on a patch that is attempting to balance out a few mons. Everyone's been going for Empyreon instead of Feraleon, so it is getting huge power as an ability soon.