Will this code adjust its alignments automatically with respect to the user's screen?
Yes 

the code will auto align to the user's browser window, as long as the browser window is greater than 1200px

Second Question

if you keep the files on your computer they will not be online, you have to host the pages on a web server and obtain a Domain name and all sorts of other stuff pertaining to attaching that site to the Domain Name and DNS Servers and such.

most of the time they will give you a root directory and as long as you keep the file structure the same you shouldn't have to change the links, you should look into absolute pathing and because I could be wrong, I usually have to check to make sure that I set my links right,  but I am pretty sure that your graphics should show up if they are in the root folder of the site with out having to change the links.

personally I would recommend that you create a folder called images or pictures or graphics  something to that effect, and change the links to images/logo.gif same with your StyleSheets those should as well be in their own folder, I usally name my CSS folder CSS