Will Pages 14 files transfer to Pages 15?

There is no real 'transfer' involved. File formats between 14 and 15 are the same - any document created in 14.x can be opened in 15, and vice versa.

Pages 15 only adds new creator functionally to aid with writing your documents, but it doesn't change the way the files are saved on disk (e.g. that Pages 15 may use Creator Studio to proofread and edit your document, fix grammar and style inconsistencies, etc., but the saved document will look no different than if you'd made the same edits manually and will continue to open and work in Pages 14.x).

So there's no real 'transfer' involved... the files on disk are identical.

Yes. Open them normally.

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What Niel said.

You have fallen quite far behind with your macOS Sequoia updates. I recommend that you stay current. Save and close all documents and applications. Visit System Settings > General > Software Update. On that panel, Tahoe will likely be the predominant offering. If you scroll down on that panel, you will see an update available to Sequoia v15.7.4. When you click that, deselect Tahoe in the subsequent panel, and only select 15.7.4 (and maybe Safari). Only those will be updated.