Yeah, this argument doesn't always hold water. If a seller could increase their price without affecting their sales volume, why wouldn't they have done so already to generate more profit? The price product of most major companies is at what the company assumes will provide them the most profit in the demand curve. So by increasing the cost for the company with a tax, it doesn't necessarily follow that the maximum profit possible will be one where the tax is entirely passed to the consume.

It’s not, but presumably all substitution products would see a similar tax, so you’re just shifting the supply curve up across the board.

It really comes down to the market dynamics for that particular product and its competitors.