When using Item Image under the image tab when entering an Item (rather than placing in the traditional Joomla way), is there any way to manipulate where the image is displayed? Currently it's at the very top and centered. Especially for introtext, we'd like it floated right, so it sits embedded in the text. The same, preferably, for fulltext placement.

Hi,
Do you mean the image position at the frontend section ?

www.ckdev.info/twt/things-to-do/eat/chefs-restaurants?start=6

On this page you'll see 2 images - salmon and eggs, and Javelinas. Is there any other location to show these other than top and center? These images were added via the image tab when adding the item.

Alternatively, if this cannot be done, can I set the image added on the image tab to ONLY show on the introtext (this page) and NOT on the details page (the page a visitor sees after clicking "Read more..."?

You can control where the image is shown (in terms of the content) through the category's settings.
You can also override the component's templates and place the image where you want it to appear. The code is well formatted and commented, and you won't have an issue identifying the block.

More on overrides can be found here: getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates