One person can build a small cabin and it has been done more times than I can keep count of.
Yes all land in the US is subject to taxes and some are even subject to home or land owners association dues.
The reason that people choose desert type spots for their homesteads is due to the climate, dry arid places in the day turn frigidly cold at night, also this weather pattern offers torrential rain, so rain water harvesting is possible,and lets not forget the abundance of solar and wind power waiting to be collected, the land itself is viewed as not too desirable by the multitude of people in the US as most places have no options for city power or water so it sells pretty cheaply.
As for the 5 bedroom home I would seriously consider downsizing to building only what you needed to live in as the rest is a waste of space, not to mention heating and cooling issues, dependent upon the type of home you decide to build will greatly impact your living comfortable and at one with the area you pick.
Ask as many questions as you like I will be happy to answer them all.
Many of use here already have our homesteads going and have our own websites dedicated to them, if you would like mine is
www.offgridhomesteading.com and you are welcome to join. I believe KatLupe also has her own.
I wish you well on your research and as said before just ask and we will do all we can to help.
Dude
www.offgridhomesteading.com