You can access your site using your assigned ip address instead of localhost. There is also no-ip.org which I assume is still around, so if you are on dhcp you can retrieve your webserver even if it changes. If your firewall's and routers are not set to block port 80 incoming (or whatever port you configured), than you can access the webserver remotely.
Modifying on the other hand isn't so easy. You'll want to use RDP/SSH or even set up FTP to allow you to modify the files.
One handy dandy trick that you may want to consider is to use a flash drive as your webserver. All it takes is a .bat or .sh file to start it up. The pro to this is the ability to move around and take everything with you in a compact fashion. The cons include slower access speeds and not being online all the time. For development environments, I don't consider either to be of relevance. I did this when I was in school; I trimmed down an apache 1.1 build and mysql 5.0, and fit that with lots to spare on my 128MB flash drive. The database is the only thing that concerned me of its growth, which when I was in school wasn't really of major concern either (so effectively I couldn't only have one project with a db active at a time). I'm not sure what the smallest flash drive you can find nowadays is; I'd guess upwards of 2gb or so :P
Even nowadays I'm still a pretty big fan of "sneaker-net" approaches.
As of PHP 5.5, the MySQL library has been officially deprecated. It is recommended to move to either MySQLi or PDO libraries for your mysql connectivity. See here for help choosing which interface you prefer: http://php.net/manual/en/mysqlinfo.api.choosing.php