If the designs are zipped, you will have to unzip/open/extract (depending on the wording of your PC's operating system) them. 

Most downloads are zipped/compressed to speed up download time.  Neither your PC nor the EM can read a zipped file.

Another possibility would be the size of the design is too large for your EM.

Message errors do not always pinpoint the exact problem. 

Most downloads are zipped/compressed files to save download time.  This type of file has to be unzipped/opened/extracted before it can be used.  Wording depends on your software program.  Once the design file has been extracted and saved and you are satisfied that you have the design along with any text (color chart, size), then you can delete the zipped file.

You also have to be sure to have the correct format for the embroidery machine.

Another caveat is to be sure the design is well within the measurement of the hoop.  If the inner hoop measurement is 5 x 7, you want the design to be less than 5 x 7 or the embroidery foot may hit the inner hoop.  Hitting the hoop will make the stitch-out to go askew, can damage the hoop or even knock off the machine's timing.

What settings did you make to your embroidery machine that would allow the designs to be accepted?  The only thing I can think of would be size or position of the design file.