yes you can, But one thing if your site visitor is to much then you cann't used shared hosting used only single hosting b'coz in share hosting your site opening page speed is very slow so you can not used shared hosting.
Its pretty much depends on your future expectation of traffic, else shared hosting would be decent enough for low traffic arcade website. And remember arcade websites requires a lot of bandwidth usage, so choose your host accordingly, and good luck.
You can use shared hosting, i do and it works fine, you'll know when its too much when either your host tells you, your site loads extremely slow, or you find from either personal experience or comments that it didnt load at all. Dedicated isn't needed for a long time usually. You'll also probably get a better answer at www.talkarcades.com
Totally depends on the traffic you're using. I know of many arcade sites that are hosted on shared plans. As long as you're going with a high quality provider that doesn't heavily oversell on their servers, you can expect good hosting for your arcade site on a shared plan. However, if you are expecting to become a very popular site with many visitors per day, you'll need to prepare to upgrade to a VPS or dedicated when the time comes.
Yes but it's rather difficult.. arcade game ext is .swf... many hosting provider will not allow it too much