The bill DID originate in the House.
Regardless of what one calls the individual mandate there are lots of other straightforward taxes (like the tax on medical devices) that are in the bill and it was treated as a revenue-raising bill in procedure at the time.
Sorry, no. No bill that imposed any tax originated in the House that subsequently became ObamaCare. The Senate adding such a tax later does not satisfy the Constitutional requirement, unless the funds collected by the tax are allocated by the law to a particular purpose or program. Such is not the case with respect to the mandate penalty, because Congress didn’t think it was a tax.