The office down stairs in front of the lifts can sort if out for you. As of a few years ago when I lived in Doi Ping Mansion, the only provider they had in the building was Sinet, but that may have changed.
Oslo Embassy - Foreigners entering Thailand by any means under the Visa Exemption scheme are required at the port of entry to have proof of planned travel (confirmed air, train, bus, or boat tickets) to leave Thailand within 30 days of the arrival date
You need a ticket out of Thailand, no necessarily a return ticket. Your airline is more likely to check than Immigration, depending on your visiting history. It is a legal requirement to enter Thailand as a tourist.
I'm sorry to hear that. As others have suggested, there are places in Chiang Mai that can provide care - it's a somewhat growing specialty in the north.