I will need Amazon EC2 for this, right?
Yes.
I want my static resources to be delivered from the CDN. Does this mean that I need Amazon CloudFront with EC2? (Or is EC2 also a CDN?)
CloudFront is a CDN, but you can use any other CDN, as with a site hosted on your own servers. EC2 is not a CDN.
I would also like to use a PHP accelerator (possibly APC), memcache, etc. Will I be able to do this on Amazon?
Yes, you have full root access to the server. You can install any software that you would install on your server.
Will I be able to use MySQL? (I ask about this because it seems that Amazon also has its own DBMS, not sure if I have to use them)
Yes. RDS is neat, but you can always run MySQL on your EC2 server.
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