In any transaction, there is no distinction between money obtained as UBI and money earned as salary. A landlord is will set his price to what he can obtain from the highest bidder regardless of source.

UBI does not generate competition. It's a supplement. All it does is translate the supply curve rightwards. While UBI might stimulate demand in the short term, it doesn't fundamentally change the relationship. The eventual outcome of sustained UBI is an inflationary spiral.