Word is essentially a word processing application aimed at putting text on a page. It is not a page layout application like a DTP program, where the text is flowed around elements on the page. Using graphics in a Word document is a bit of a fudge and it does have a tendency to screw up documents that are subsequently re-edited.
http://www.gmayor.com/extract_images_from_word.htm should help with the image extraction.
Snagit will help with the screen capture and borders.
Captions are just indexed blocks of text. Who's to say how a previous user may have manipulated the text strings to get the effect they required?
The default insertion method is in-line whereby the image behaves as a large text character. It becomes part of the text and will remain where it is placed relative to the text, but can leave image height gaps where the image will not fit on the page and text flow moves it to the following page.
Floating images, such as those you describe, are anchored to locations in the text area of the document but are in a separate graphics layer of the document. As they can move around with the text and even get moved off the page, it is best to add them after the document text is otherwise finished.
Floating images are usually anchored to a page location to avoid them moving, but this means they may not reflect the adjacent text which can thus move around them. They may also be anchored relative to the text Floating images are best avoided where possible as they can all too easily behave as you indicate.
There's a third option for wrapped images, I would suggest using a frame to hold the image and its caption. Images are inserted inline in a frame and will shrink to the width of the frame. A caption added to that image will go in the frame, increasing the frame height as required. You can then wrap the text around the frame using the frame format commands.
Frames are an all but hidden feature in Word, but you can add the 'Format Frame ...' command to the QAT (Quick Access Toolbar) from the all commands group for ease of access.
If you have added a border to the image with SnagIt, you can display the frame without a border.