I think what you’re describing is more or less possible with forms in InDesign.
You can anchor a text field in InDesign to a table cell. That’s easy to do, and the text field would then move around with the cell.
To get the text field to exactly fill the dimensions of the cell and change in size if the cell is resized is not a built-in feature of InDesign.
However, it should be possible to automate – meaning that if the size of cells changes, you would run a script on that table and all text fields would resize themselves to the new cell dimensions.
I wouldn’t recommend using the idea of converting a table cell to a graphic cell and then turning it into a form field, because you would lose too many features of FormMaker that way — they all rely on the fields being text frames, since that is the only way to apply formatting such as font, colour, alignment, and so on,in FormMaker.
So again, I would keep your fields as text frames in InDesign. Copy and paste a frame into each cell. Run a script which I can provide to fit the size of the frames to the cells in the table.
I think that would be almost as easy as it was in LiveCycle!