Eloy,
There's probably a handful of things that are playing a role in your confusion. You should be all set with software (although you can use up to GPScorrect v3.16 with ArcPad 8), no need to install or upgrade anything.
First of all, prior to ArcGIS Desktop 10.0 there were two toolbars which you could use to check out data for ArcPad. The first was the short, 3 button toolbar called the "ArcPad toolbar". This was the very first toolbar that was released when ArcPad first hit the market. It did not require that you save your mxd and it allowed you to check out / check in edits from data in shapefile format OR data within a geodatabase.
With the release of ArcPad 7.1.1 we introduced the "ArcPad Data Manager" toolbar. This toolbar will only check out and check in edits from a geodatabase (you can check out shapefiles and edit them, but their edits cannot be checked in and reconciled with the dataset it came from) and stores the data in an axf file. At ArcGIS Desktop 10.0 the ArcPad toolbar was deprecated (because of a lack of support for functionality written in VB) so you're forced to use the ArcPad Data Manager toolbar.
An axf file is a small database format based upon Microsoft SQL Server Compact Edition.
To check out data which you intend to edit in the field and then check back into the database it came from, your data must be checked out using the option "Check out for disconnected editing". If you attempt to check out your data and don't see this option, it means that the spatial reference of that particular feature class does not match the spatial reference of the data frame of your map document.
You'll also see options for "Background Shapefile > Editable" and "Background AXF > Editable" but don't let this fool you. You'll be able to edit that data in the field, but you WON'T be able to check it back in. You'll just be left with a stand-alone file.
Based upon the information you provided I'm really not sure why you were getting the errors that you were seeing. I'm also not sure how you were copying the data over to your mobile device, but I would suggest that you manually copy and paste the data (the output "DataForArcPad" folder that is created by the wizard) from your desktop machine to your mobile device via ActiveSync.
I would suggest that you create a brand new feature class in your geodatabase and run it through a test check out. Check out the data, copy to your mobile device, open in ArcPad, make an edit, copy the data back to your device, and check it back in. At the point you get this process working successfully on a new feature class, start testing with your existing data.
Another test you can do is to open the axf files in ArcPad on your desktop machine. Do they open there but not on your mobile device? If this is the case you'll want to make sure that you have installed "SQL Server Compact for Windows Mobile" via the ArcPad Deployment Manager.
If you go through this process and have any more questions or problems, please feel free to respond with as much info as possible and we can get you moving in the right direction.
Thanks.
