- Is the baggage allowance United is explicitly showing me here accurate? I'm UA Premier Platinum, but it lists the same charges for general members.
First bag allowance is correct for award ticket.

- I'm not seeing the $100 fee for a second bag on SWISS' excess baggage page (sorry forum won't let me post URLs), where does this come from?
If you are Star Gold and if you have booked an award ticket there is no fee for a second bag. I think currently the correct fee is somewhere around 25 CHF per direction, if no status and not light ticket. United's $100 fee quote is wrong.

- According to United's booking page, the first bag is free but the second is paid. If this is an Economy Light fare, I would expect to pay for both bags. However, if this isn't an Economy Light fare, then I would expect to have two bags free as a Gold member. What kind of product am I booking here?
Award is not light, i.e. includes (at least) one piece of hold luggage.

- Who is accountable if I show up at the airport and they will try and charge me for a bag?
They won't