Select by text attribute and apply a style

Although you can certainly determine what words of body text are a specific font size, you won't be able to select them for further interactive action from the Pages interface, or apply a paragraph, or character style, because the AppleScript Dictionary support for Pages v8.1 does not support this behavior. In general, it is a small figment of the prior AppleScript Dictionary support found for Pages '09 v4.3.

From a productivity standpoint, you would be better off in Word or LibreOffice with their extended Find/Replace facilities that do support styles.

If you want a detailed answer you need to provide details of what you are talking about.

Principally what version of Pages on what version of macOS.

I am going to guess that you are talking about Pages 8.1 in a late version of macOS probably Mojave.

Q1 No. With an outside chance that an AppleScript might fix it

Q2 No.

Q3 Possibly

The reasons are that all versions of Pages 5 to 8 lack the features of Pages '09 that let you find text with a ceratin attribute and then apply either a Paragraph Style or Character Style to it. They also lack the ability to select non-contiguous text. To cap it off Apple has given them inadequate AppleScript support.

There is a long list of missing features that have meant that Pages 5 to 8, along with the companion Numbers and Keynote, have dragged down the iWork productivity suite for the last six years from a level of marked superiority to a sop for Mac users who did not want to either pay for or put up with MsOffice.

Your choices are to use Pages '09 which will soon become unusable in macOS Catalina unless Apple pulls a rabbit out of the hat, Put up with Pages 8.1 in the hope that Apple will fix all its shortcomings when Apple has dragged its heels for 6 year, or switch to something else.

Unless you tell AppleScript to change the font face, size, or color of a word in the Pages v8.1 document, you won't see any visual trace in the document that the AppleScript has run. Thus, you cannot get or set the current cursor location, or get/set a given page number. AppleScript is not an extension of the Find/Replace tool where you see the selections that match, and can interact with them.

From a user prompt, AppleScript can take in a word and attempt to match that word to a list of all words that may match a particular critieria (e.g. font-face, font-size, color). Then if it is a unique word, and you have the index of where that word was found in your list of all words, then you can tell AppleScript to do something that it is allowed to do — with the next adjacent word. This wouldn't be much fun to program, and the program would be slow. This is all theoretical.