I recently upgraded to version 4.
Yesterday, I mistakenly opened up the version 3 icon and put in several hours worth of image work, metadata changes, and created a couple of collections.
1. What will be the easiest way for me to update the changes to my version 4 catalog without undoing work that I have done in that from the last couple of weeks?
Backup your LR4 and LR3 catalogues, so you'd be able to get back to the current state if everything went wrong.
Now in your LR3 catalogue, identify the images you've worked on (eg by selecting the collections or with a smart collection using Edit Date as a criterion). Select the affected images and do File > Export as Catalog. Save it onto your desktop.
Open this exported catalogue in LR3 and review it. You may have collections you don't want, or other info. Then close it.
In LR4, do a File > Import from another Catalog and bring in the catalogue from the desktop. Now, the danger is where you have changed the same image in LR4 in the last two weeks, and also changed them in LR3 in the last day or two. If so, then check the option to create new virtual copies and then resolve them one by one with Sync Metadata/Settings. If not, the imported catalogue will update pictures in your LR4 catalogue.
Plenty of backup, and proceed slowly.