#2013 error when starting the dev desktop
Your first error seems to be related to a problem with port numbers/bind address of the MySQL server; see this post for a bunch of suggestions for a fix.

The second error is a permissions issue; you need to give your web server user write permissions over the "sites/default/files" folder, for example using the following command:

chmod -R 755 /path/to/root/sites/default/files


If you don't know how to do it I'd really advise getting someone who does to help you, that's messing about with POSIX permissions and you need to know what you're doing or things can go horribly wrong.