I recommend to ask in the AEM Forms sub-forum: https://experienceleaguecommunities.adobe.com/t5/adobe-experience-manager-forms/ct-p/adobe-experience-manager-forms-community (Unfortunately I cannot move this post there ... @kautuk_sahni can you help here?)

You don't need to ship it, as the core components are part of the product. And of course all backwards compatible changes on the components themselves are versioned, so you still use the v2 page, although the core components already have a v3 for it.

IIRC DynamicMedia requires a dedicated license. But I am not familiar with licensing aspects, sorry.

If you want to write the short-path as URL within the page itself (or a different page), just write the "long" path there. If a mapping exists AEM will do that for you automatically. At least for pages, not for JSON payloads etc. For these you need to use the ResourceResolver as indicated above.

What password are you using? You cannot do a POST of your AEM credentials (which you enter either at IMS or at the SSO solution of your company) to AEM, that won't work.

What type of authentication (and therefor: credentials) are you using? JWT token? Username/password as basic auth? (Remember, that in AEM as a Cloud Service the authentication normally works using IMS and tokens, unlike the "classic" way of using username/password).

For reference: If you use the latest Core Components and Dynamic Media, a WebP image will be delivered by DM if the browser can handle that. And to make that work you don't need to do anything (but using DM and Core Components).