You can do as you intend, with some code restrictions.
You cannot tap off a kitchen/DR/nook of similar circuit. Nor can you tap off a bathroom receptacle circuit.
Outdoor receptacles must be GFI protected. It is always easiest to have a GFI device where you need it, as opposed to a GFI breaker.
You certainly can have more than one GFI on a circuit. For one thing, you can wire them all to "LINE" side and they will all simply protect themselves. If you do "LOAD" out to other GFIs there is very little chance of nuisance tripping. The more sensitive one will simply trip. This is a common DIY mistake but is not a code or safety problem, just a convenience one.
If the home is vinyl sided Arlington
makes some very cool products that will make the job much easier. Go a to a real electrical supply house (or the internet) to see what they offer.