1) Starting with 400 DPI image 3000 X 2000. Can I ignore DPI and just adjust pixel size to whatever I need? If CP product template uses 3000 X 2000, can I leave DPI at 400?

2) Also, I want to shrink it. Can I simply do math (pixels/DPI=inches), so if I want 7 inches wide, x/400=7 so x=2800 pixels. Or can I just type stuff into the resize box of Adobe PSE7?

I guess I can also use the crop tool if there's an area I can remove, but if not, I have to resize.

3) Finally, what's the best way to take an item in a photo a make it fill the canvas? Crop it out then resize it or enlarge the whole image first then first then crop? If starting with 400 DPI, is it OK to change it to 200 DPI to enlarge it and then cut out the part I want?

Maybe I should hire someone?

"ignore dpi, pay attention to pixels"

you can reduce the number of pixels in an image without serious quality compromise (to a point)

increasing number of pixels in an image always involves "inventing" information that was never there so quality will be an issue.

What Tanith said

So...
1.) Yes.
2.) Yes you can shrink it in that example. However if you want the image to be in the same aspect ratio then you don't need to shrink it. If you want it to be different though, Example: longer on one side and shorter on another than the original then you'll want to crop it.
3.) It depends. Sometimes I add black or white "matting" around a photo and even add in the photo's title, etc.

If starting out with 400 dpi you can change it to 200 dpi to "enlarge it" and then crop out the part you don't want.