Hi and welcome to the forums, I will try to help you with some of your questions:
1) Personally I save my projects from MPC to my ArcGIS server, not to ArcGIS.com, so I can't give you much help there, but I do suggest using your own server for now.
2) Not sure about this, could be just limitation of the device or lack of internet connection (speed) on the mobile device.
3) Windows Mobile crashes a lot, I have one of the earlier builds and I have noticed this and made a post about it. If you download the latest build, it is said to increase the stability of Windows Mobile. Note you may want to try the Tablet version to get some understanding or play around with it.
4) I know it has been said to use the GP tool to create a cache and upload them to your mobile devices. In my situtation I don't have to use GP, I can connect my mobile device (Tablet via ethernet and Window Mobile via USB using MS ActiveSync). Then Synchronize the data and then disconnect the devices and use them. I have found this to be much faster than manually creating the cache and then putting them on each device.
For now, you may just want to take some of these steps I did so that you can start to see how ArcGIS Mobile operates.
Please do ask if you have any further questions.
Good Luck!