See the attached. This is the combined dataset for just the first shapefile, into a file gdb.
Here is the process I did and it was pretty fast
1. Open ArcMap, load the first shapefile
2. Export this shapefile to file geodatabase (you may need to create this first).
3. In ArcMap, only have the file gdb feature class in the Table of Contents, then load all of the other shapefiles of just that file (so, the first one).
4. Open edit session for the gdb feature class.
5. Select all records from the next shapefile (like from folder two) that you have in your TOC, and then go to Edit --> Copy and then Edit --> Paste and select the feature class to paste into.
6. Repeat that for the next 8 or 9 shapefiles.
This worked for the first shapefile.
But, like Benjamin said, many of these shapefiles have broken tables which would be why you are getting errors. You may need to find the source of the data and verify that they are valid shapefiles (with good tables).