You're pointing out issues that aren't actually related to UBI. In a properly functioning real estate market, if rents rise to the point where landlords make easy money, more housing gets built and the effect diminishes. The problem is most metro areas have stupid housing and zoning policies so even without anything like UBI we already have massive rent inflation. Fixing the housing situation would largely diminish the potential for UBI to create massive rent increases.
Healthcare is also its own problem that is widely discussed on HN. Any sane national healthcare system would largely prevent huge increases in healthcare costs. Our privatized system is just a horrible model all around.
Also, it's worth noting that most UBI proposals include indexing the UBI amount to inflation, such that if UBI disbursements do lead to inflation, the UBI payments go up to account for it so that UBI recipients are at about the same means on a year-to-year basis.