Calculating power needed for a mercury-vapor bulb
Watts = Volts x Amps. Wh = Watts x hours. Your 'solar panel' can (perhaps) generate 5V x 2.1A = 10.5W. 98Wh / 10.5W = 9.3 hours. That would be at least two days of typical sunlight. 

To charge your '11V' battery you need a battery charger designed for your battery type (lithium-ion?) and nominal voltage (11.1V?). The charger wastes some power (perhaps 20%) and probably needs a higher voltage to operate from, so you may need a voltage booster which wastes more power (another 20%?). So in practice it will probably take ~15 hours or 3 days to charge your battery (if you don't use it in the mean time).   

Your 100W inverter can output 100W maximum. But your lamp needs 160W. So you will need a more powerful inverter. 

The inverter wastes some power (20%?) so the battery will have to deliver ~20% more power than the lamp needs, ie. 192W. 192W / 11.1V = 17.3A. If your battery isn't rated for this much current then you will not be able to run your lamp from it. 

Assuming your battery can deliver 17A, it would theoretically last 98Wh / 192W = 0.5 hours or 30 minutes. In practice you might get 80% of the rated capacity ie. 24 minutes - after charging the battery on the solar panel for 3 days.