I followed your suggestion of creating a second style. Nevertheless, now my caption is in italic even though the respective style is formatted as nonitalic. It works but it is not pretty. Is there a way to tell Word not to format captions (or any other labels) as italic, so I can have my style format the text as italic?
Yes, you can modify the Caption style to remove the italic setting. To do that, start by clicking in any caption that is now italic (without any other formatting applied to it). In the Styles gallery on the Home ribbon, click the bottom one of the three buttons at the right end of the gallery:

which opens several lines of styles. One of them will be the Caption style. Right-click that Caption style and click Modify in the menu.

In the Modify Style dialog, click the
button to turn off italics, and click the option button at the bottom of the dialog labeled "New documents based on this template" (that will make the modification in both the current document and its attached template, probably Normal.dotm). Click OK. All of your captions in the document should immediately become non-italic, and the same will happen in any new document you base on the same template. (It will not change any existing documents, which would have to be modified individually if you need that.)
Also, I wanted to change some of my styles to character styles (those that shall not apply to a whole paragraph). Having said this, the mentioned drop-down menu is greyed out for me, any advice on what to do here?
Once a style is created as a paragraph style, it cannot be changed into a character style. (I don't know why, but that capability was never programmed into Word.) During the creation process, though, there are two distinct ways to create a character style.
- When you click that third button on the Style gallery as in the screen shot above, one of the choices is "Create a Style". That opens a small dialog box titled "Create New Style from Formatting".

As it says between the two text boxes, this is for creating a paragraph style; if you change the name and just click OK, you get a paragraph style, and there's no way to change it to a character style. However, if you click the Modify button instead of OK, it opens the Modify Style dialog (misleadingly titled "Create New Style from Formatting") where you can change the style type to Character and select whatever formatting you want.
- You can open the Styles pane (Ctrl+Alt+Shift+S). At the bottom of the pane, the leftmost of the three buttons is the New Style button. Although it uses the same icon as the Create a Style in the previous bullet, it uses a different internal command. It directly opens the Modify Style dialog (again misleadingly titled "Create New Style from Formatting") where you can change the style type to Character and select whatever formatting you want.