From what file type are you importing? IS this a tab, csv, excel or other file type?
It appears the problem is with the format of that file and the specific file type that you are selecting for your import. Example: if you selected Tab as the file type for your import, there needs to be a tab character between each column of data to be imported and a return between each record. You'd get what you describe here if the data that should import into separate fields is not separated by tab characters. Missing commas for a csv import would produce the same result.
And you can drag the fields on the right up and down to align them with different columns of import data on the left in order to get the correct column of data into the correct field--but only if FileMaker can successfully parse the data to import into the correct columns and this will depend on the format of the data in your file and the options you select during import.
I appreciate your help, I think that really helped and I will look into this and come back here to let you know.