We have multiple SharePoint 2013 sites and we want to know if it is possible to upload a new file for the first time, one time, have it upload to multiple sites within the same collection. Also, we would like to tag it with relevant tags at the time of the multiple location upload.

Is this something that SharePoint is already capable of or does it require development.

If it requires development is it SharePoint Designer work or deeper programming?

Its not designed to do that out of the box.  One of the key design goals behind any database project is to never store duplicate copies of something if it can be avoided because that opens you up for potential errors.  The same is true of SharePoint.  You may be able to do it using custom code, but I don't recommend it as a design.  Once the file is uploaded to multiple locations it will inevitably get out of sync and users won't know which one is the right file.  Upload it to one place and then link to it from the others.