I tried highlighting the word I wanted to style, but the entire paragraph changed style. Why would my custom style work any different from other styles like underlining, boldface, or font change?
Use Character style, not Paragraph style. Different style categories are listed at the top of Styles pane (F11).
@contestcen: If you are accustomed to the simpler world of MS Word styles, the separation of style categories in Writer may be confusing in the beginning. I suspect that you will learn to appreciate the LibreOffice way of styles handling, in particular for more advanced document structure (content or design).
I have never used MS Word. I recently switched from OpenOffice to LibreOffice. I chose the style I wanted from the dropdown list in the upper left corner of the screen, to the left of the font list. It lists dozens of styles, including the style I wanted, but there is no indication of paragraph vs text styles. (F11 does not do anything.) I managed to find the panes you mentioned by selecting Styles > Edit Styles, but this is an inconvenient way of getting a style, since I don’t plan to edit the styles. The OpenOffice method of Format > Apply Styles seems more natural.
It seems to me that it would be much easier all around if the styles pane appeared whenever you clicked Styles on the toolbar.
Do not answer a question unless it is a real answer (and yours is not). If you have reasonable suggestions about LibreOffice features, file RFE(s) at Bugzilla.
@contestcen, why do you think the developers should do the program the way you imagine?
If you have good suggestions you can register them on Bugzilla.
However, you could alternatively try to understand what the developers have created and how it has to be operated. The help here is all related to the latter.
If you also want to know how the program works, you can learn a lot from the documentation here. I wish you success!