Hi @georgey82106871
Those are many different questions and I'll try to examine them one by one, which should help in getting useful comments and answers by other forum members. Your main issue is rather common: making your captions (and keywords) from your Elements software accessible to people having only the standard Windows tools: Explorer, Photos, Gallery...
In random order:
1 - Since you mention that those people publish to the web, they probably have also their own photo editors. Practically all those editors have more functions that the Explorer and can retrieve all captions and keyword tags saved into your files. So, let us concentrate on those who only use the Explorer.
2 - By default, your captions or tags are recorded in your catalogs (I assume you are using the organizer) and only saved into the media files if you issue the command 'Write metadata to files'. This is not new. The captions may be written directly into the files as well as in the catalog when they are created, but since keywords are at least as important, you have to always write metadata to files as a rule.
3 - In the Windows Explorer, your recipients have to know how to get the caption from a file: it's from the properties panel, section 'details', line 'Title'.
4 - You have found that the png format does not support writing metadata to files. Yes you can use tiff or psd, but why not jpeg?
5 - If you use the organizer, you can write metadata to files in a single command for as many selected files as you want, if they are in a compatible format, that is NOT png.
6 - For raw files I imagine the problem is that the metadata are not written directly into the raw files but in sidecar xmp text text files. That requires a raw converter/editor for your correspondents. You are right that the best solution to include your metadata within the files themselves is to convert to the DNG raw format, which is also more widely understood than proprietary raw formats.
7 - When you tag your raw files, the metadata are kept either in the xmp sidecar files or in the DNG raw files directly.
To batch convert your raw and dng files at the same time, the organizer does not offer the option to convert to the DNG format, but the Camera raw plugin dialog has this ability. Depending on your amount of RAM you can open a batch of 20 to 50 raw or dng files you have tagged in the editor ACR, select all and use the 'Save' button to export them in a new folder.
Can we start from here?