What PHP version will I be running?

I know Stanley gave you a good answer, so I'll just address your questions specifically.

• what PHP version would I be running If I am just writing PHP commands within sublime text?

• At this point is version independent, unless you're using parts of PHP that were only available in certain versions of it, you'll want to be aware of this. You should catch these errors when you go to a staging server though, as it'll become obvious you have an error

• Does the browser assume I am using the latest version?

• The browser has nothing to do with PHP. It doesn't care. The browser only deals with the HTML, CSS, and JS of your website. When the user makes a request, the browser sends that request to your server, where the server would process the request, parse any PHP you have as part of that request, and return to the browser only HTML, CSS, and JS

• If I were to upload these .php files to a server, what version would it be running?

• Depends on what version of PHP is installed on the server. Most hosting companies are going to do this for you, will not allow you access to it, and will update versions pretty quickly after a new version is released. Some situations like a VPS (virtual private server) or a dedicated server will allow you access to install and maintain whatever version of PHP you want, along with all of the other software pieces need for a server.