How to convert InDesign picas to Pixels for Photoshop?

You can set both Photoshop's and ID's rulers to pixels by control clicking them, and in ID you can get a picture frame's dimension from the Transform or Control panel:

In Photoshop you can set the crop tool to your frame's dimensions leaving the Resolution field empty:

The cropped image will fit exactly into the ID frame:

It is vital to know the intended purpose of the document in order to know how to advise you here. As Michael an Willi have pointed out, pixels have no physical size on their own, and the same image pixles can be compressed or stretched to different size containers without changing the data in the pixels by changing the resolution. What they haven't mentioned is that different outputs require different resolutions for a satisfactory appearance.

Resolution in Photoshop is just a placeholder. It tells other applications what physical size you intend the image to output, if they do physical output. You can change those physical dimensions in Photoshop (or by scaling in a program like InDesign) without resampling, and you'll see that the image size dialog reports exactly the same pixel dimensions, but changes the ppi value reverse-proprtionally to the change in physical dimension, and there will be no change at all to the image itself in Photoshop. My favorite analogy for this is printing on a balloon. As you inflate the balloon the image stretches, and the resolution goes down (the same pixles are stretched to fill a larger space, so there are fewer of them per unit), and as you deflate, the image gets smaller, but the resolution goes up. The printing on the balloon never changes.

Back to how much resolution do you need? The answer is it depends on the image and how it is used, the printing method, and the viewing distance. Close-up viewing like in a book requires much higher resolution than you need for a billboard seen at half a mile, and a semi-transparent background image is probably acceptable at a much lower resolution than the portait of the CEO.

All of this is a long-winded way of saying it's not enough to set the image size in Photoshop to match the frame size in ID. You need to also look at the pixel density at that size and make a determination if that density is high enough to prevent your viewers from seeing each pixel as an individual block.

Which units Id uses can be selected in the preferences or with right mouse click on the rulers. There are not only picas, also mm, cm, inch, points, ag and pixels.

But with Id comes also resolution as pixel per length unit (mostly ppi) as important factor to the size of images.

Pica is a length measurement, pixel not. So it is difficult to compare. Pixels are the smallest part of a picture, picture element. This does nothing say about physical length or size.