A library (your iTunes folder) consists of parts, just like a city library. Media are only part of it. Media alone are like books sitting on an empty block in the middle of a city, no building or librarians. What gives it the structure you see is the iTunes Library.itl "catalog" file working together with other files and folders in the iTunes folder (e.g. artwork is stored in a separate location). If these were stored on your old computer then you have a pile of media. Normal practice is to also copy the iTunes folder to the new computer so iTunes knows all about the existing media on the external drive.
About iTunes library files - https://support.apple.com/HT201610 - Does not mention that a complete working library also includes other files and folders also in the iTunes folder.
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
Where are my iTunes files located? - http://support.apple.com/kb/ht1391
iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847 - plus supplemental information about organizing to new structure https://discussions.apple.com/thread/6477809?answerId=26404702022#26404702022
Since the rest of your library was missing iTunes created a new library (it is strange it added a "1" since it only does that if you deliberately created a new library next to an existing iTunes one but maybe you aren't telling us something) and did its default thing (unless you changed settings) of copying any added media to the Media folder inside the library folder. If you didn't want it to do this then you should have changed preferences for the media folder location in advance, or better yet put the entire library on the external drive.
As to why only some of your MP3s appear you will have to tell us more. MP3s usually store the track information in each file so if they were added they should appear. Were they all added? If not, it is possible I guess that too much was added at one time and something slipped up in the system, or a bunch of other guesses I could make.
