Can I put my Poser in C:/Programs since I put my content on an external drive.

Yes. I do suggest that you NOT put the included content in that directory, however.
And I don't remember, do shaders also need to be in the app folder to work? Or can I put them on my external drive?

Shaders can go anywhere. PYTHON scripts MUST be in the Poser:runtime:Python folder/
Can I just install the 64bit app? 

Yes
Do I have to install the content that comes with Poser with the program install or can I go back and do it later?

It's content. You can install it at any time. I do suggest that you go ahead and do it, because the default Poser scene includes "Andy", which is part of the content collection.
I'll also need the SR, can I download that to any folder and run it, or does it have to be in the app folder?

The SR can be anywhere on your drive.