I have used resource layout painter from my desktop to design a html page that displays drop down boxes and a report. runs okay on my desktop.
I now need to have this run as a self service appliction on a webfocus reporting server. I have many self service applications currently running, none have been done with resource layout painter before. Can the new fex and html files be copied to the webfocus reporting server? Not sure how this works when resource layout painter creates the html code.

Depends where you are create the Resource Layout page. If you are already in an application on the server, then just point a URL to that page. Http://servername/approot/appname/filename.htm. If you created it in MRE, you cannot just copy it to self service without editing the htm. You want to create the Resource layout page right on the server. Hope this helps.

The only way I can create the resouce layout page on the server would be in mre. So if I create the resource layout page in mre then I will need to edit the html before it can run as a self service application outside of mre. Is that correct?

If I create the page in mre then I will also need to move the fex's that are executed in the page into mre. Then I will need to move the fex's and html page out of mre and into my self service directories and edit the html page that is generated by resource layout painter. Is that how this is done?

You don't want to do that. If this is a self-service app, then create it in the apps directory. If you don't have access to the server, then that's a problem. The alternative would be to create a local project and deploy.