heyy
Welcome . .
Is this a new Mac from the store or second hand from someone else ?? What type of Mac and what OS are you running ??
Can you give us more info please on Mac specs, and on the downloading? What are you downloading ? From where ? Where have you got your downloads going to ? This can be set in Safari>Preferences>General and down the bottom of the page there is a drop down to pick where your downloads go. If your using safari to download. Have you tried a different browser ??
To me, it sounds like you are getting a corrupt download, and its not complete. First thing, i would try Repairing Permissions via Disk Utility, log out then back in and see if that makes a difference.
Cheers