Income tax rate is flat at 15%. There is also 14% health controbution, capped at HUF 450,000.
Income for property rental is usually subject to the above BUT for short term rental you have the option to pay instead a yearly flat tax of HUF 38,000 per guest room.
Also, health insurance should not apply if you are not resident in Hungary.
http://www.budapestinvest.net/budapest-property-taxes/