Is it possible to add buttons and forms content into table cells?

Buttons: don't!;

Forms in a table: yes, possible (even will be accessible for WCAG!) through anchoring. 
Forms will work fine in iPDF(!) buttons will not; forms will not work in Publish online.

I'm going to throw cold water on this before you spend hours or days on it. You'll never get what you want here in a PDF and Publish Online does not support forms.

My standing advice is to create a from on your website and be done with it.

Hi @Trey138 ,

you could try two things with forms and table cells, I think, but did not test with current versions of InDesign:

[1] Anchor form fields like buttons to text cells.

[2] Convert a text cell to a graphic cell and convert its contents, an empty graphic frame, to a form field like a button.

But I do not think, that you can use live, editable text inside a graphic cell. The developers made this unavailable because of a severe bug with graphic cells that could crash InDesign. This bug was never fixed and dates back some years…

But I have no idea if the form fields will work as expected when exported to PDF.

Try that as Derek suggested with Publish Online.

Regards,
Uwe Laubender
( Adobe Community Expert )

Best not to use PDF for this as, apart from other issues,  you can't control the various PDF reader that users may use that aren't compatible. Have a look instead  at InDesign's Publish Online facility,, which might be able to offer the features you need. And, as the output is HTML5, the documents can be read on PCs, Macs, Tablets and Smart Phones with a compatible browser .