Usage of file extensions as nouns and verbs

Current convention in technical writing is to use lowercase for file name extensions. Both the Apple Style Guide (page 8) and the Microsoft Manual of Style (page 122) request writers use lowercase for file extensions and to include the dot.

Files ending with .pdf are read using Adobe Acrobat.

Additionally, the Microsoft Manual of Style suggests using descriptive terms when writing about file types rather than reference them through the extension which includes making them into verbs.

Convert the file to a bitmap file.

When writing for end users in manuals and instructions, I break with Microsoft (a smidge) and reference the file extension too because users are more familiar with the file name extensions than what the extensions represent.

Convert the file to a bitmap file. The file name extension will be '.bmp'.

Casual constructions are often not understood by people who do not speak and read English natively. (The Global English Style Guide) This is true even in casual internal communication.

This is a relatively new field, and it's more a question of stylistic choices than a fixed set of rules. Perhaps an established set of conventions will come in time, but for now, you have to use your judgement. For what it's worth, here's my judgement:

Are file extensions to be capitalised (e.g. PDF file, JPG image or pdf file, jpg image)?

Yes, it works best to capitalize them, as they are easier to read in this form, and they are mostly abbreviations anyway (acronyms or at least initialisms).

What about making them into verbs?

Yes, it's natural to do that, where practical. PDFing, PDFed seem the most logical forms to me. (Apostrophes are not needed.)

should the file extension be capitalised in this case?

It's much easier to read these words with capitals, so I'd argue yes to this.

what are the rules on redundancy when calling it "PDF format"? Is it bad style to do so?

Ideally, avoid redundancy like that. It's better if the original meaning of the abbreviation is kept in mind, although, inevitably, it will be forgotten over time. Usages like "ATM machine" are all too common. (I even include "the hoi polloi" amongst such howlers, but that's a different matter.) So it may be a losing battle, though that's no excuse to get it wrong when you know better. It's easy enough to rephrase "PDF format" to something like "as a PDF" etc.