I keep my rates the same for simplicity, with the exception of Airbnb where I show a different rate that is inclusive of taxes as they do not separate out the taxes like other OTA's
Not sure but you may be contractually obligated to do the same rate. You can for sure not offer lower rates on your own website.
You would only be obligated to honour a lower price if you personally set up that lower price promotion.
Not sure where you are, but I often find it confuses some of our potential guests from the US as they advertise in US dollars and we are in Canada so it always seems to show a different rate.
Regardless, we still get our true $ CAD rate per room
Not sure where you are located but I use 1 866 492 3245 for customer service regarding any bookings.
For the online payment I think if you go to your extranet and click on the "opportunities" tab there is an option in there to select the option "reduce cancellations by letting guests pay online"