Your power requirement approximately equals as follows:
1 fan = 95W
1 light = 60W
1tv = 200W(CRT)
Total = 355W.
This inverter can provide load up to 550W. So it depends on the size of the battery how much time you get backup. Considering a 150AH 12V battery the backup time can be calculated as follows,
Time = (150*12)/365W = 5hours approx