Have image with a figure # and text reference

Hello!

I have what will be a very long InDesign document with a LOT of images.  I've just started the document and may need to reorder the images over time.  I need several things:

1. I need each image to have a caption which begins with "Figure 1: blah blah" and if I move the image, the caption should automatically re-number.  I think I have the automatic re-numbering working using paragraph styles, but doing that seems to prohibit the other things I need to do, such as...

2. I need to have each image coupled with an in-text reference, like. "As seen in Figure 1, blah blah blah."  And if I move the image, again, not only would the caption re-number but the in-text reference to it would re-number automatically, too.

3. Finally, that in-text reference should automatically also be a link, so if the text is clicked on, the person shoots down to the referenced image.

Is all this possible in InDesign?  I've been using InDesign for over a decade and never have figured out a way to get all three of these requests to work.  It seems to only offer 1 of the 3 in the current set of tools.

Thanks!!!