Switching to PHP 5 is done on your server, please contact your host on instructions on how to upgrade your hosting.
Upgrading from 3.6 includes some major changes, so you should expect quite a few template changes. I am not sure how much the CSS has changed, but I would recommend you duplicating your live site (in terms of styles, settings, and plugins) and do a test upgrade. This will give you advanced knowledge of the problems and you'll be able to fix them before doing an actual upgrade.
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