Hi Jane,
You do not say what OS you are on but I think I can answer most of your questions:
—Things not showing up in Thumbnails: My guess is that your cache for this needs to be rebuilt. To do that, go to Tools (menu) -> Cache -> Purge Cache for (the folder you are in). If you want, you can expand on this and do -> Cache -> Manage Cache and select the bottom option "Clean up Cache (and -Purge all local cache files).
—If you've made a correction in Adobe Camera Raw and are now looking back at the thumbnails in Bridge, you will see a little icon in the top right corner of that image showing if there's been any alterations and/or cropping in that image. If an image has any changes, right-click (or Control-click) on the image and scroll down until you see "Develop Settings" then select Copy Settings and then re-right-click (Control click) on the images you want to change and select Paste Settings.
—If you're in ACR and wish to do this and you've opened up a number of images in ACR, your primary image will either be on the top or on the far left. Either way, do a Command/Control-a to make all of the images active and then click on the elipse for a drop down menu and select Sync.
Bridge cannot crop. You need to be either in Photoshop or ACR to crop. At this point I guess I need to know what version of Bridge are you looking at and what version of ACR you're looking at. And while I'm at it, what is your OS (and what release)?
Good luck!