It might be best to spread those questions out over a couple of posts, Dr. Pete. Not only will it make it easier for us to answer your questions, but it will certainly save wear and tear on your scalp if you don't save your questions up and ask them in batches.
That said, there are solutions for some of your challenges -- though not all.
1) You can usually position the text blocks in a title pretty accurately. You can also set them, using the Toolbar, to center align vertically or horizontally. You can't nudget them using the arrow keys but, if you zoom into the monitor, you can usually position them within a pixel of where you want to be.
2) As for resizing photos -- no, the nature of the program is that, as you drag the corner handle, the entire image gets bigger or smaller. You can't get it to expand only to the right and down. However, if you right-click on a photo or any clip on the timeline, you can Show Properties and, in the Motion properties, set the image's Scale very precisely.
3) Stroke and drop shadow effects should work on any shapes you draw in the Titles workspace. However, they will only be adjustable on text that has had a Text Style applied which includes stroke and shadow. (Though you can customize the font afterward and even save your own custom style.)
These are pretty fundamental questions, by the way. Are you looking for some basic training or a book on the program?
You and Dr Pete forced me to go to PE and check out the "nudging" of type. In PrPro's Titler, the cursor keys DO nudge the type. You are correct that in PE they do not. Learn something new every day!
For a good book on PE, I strongly recommend The Muvipix Guide to PE7. You can obviously see who has not completely read HIS copy of the book. I keep finding out differences between PrPro and PE, almost every day.
As for the Scaling of a still image, it's easy to do in a two-step process, though not as one would with say a Layer in PS/PSE (the method that Dr. Pete was attempting to use). Do the Scale operation (all four corners being affected) and then use Motion>Position to place the image in the frame, where desired. Not as easy as a Shift-drag, but the result will be the same. As Steve mentions above, within Properties, the Motion>Scale AND the Motion>Position can be set critically and exactingly. One can also do the operations by Click-dragging. Just two steps, instead of one.