You need to do some math.... Assuming the solar panel outputs 12v, 50w/12v= 4.1 amps. If it charges for 12 hours on a sunny day 12 x 4.1 = 50 amp hours (ah).
Then you need to figure draw...how many lights, how many amps each, how long will water pump run, etc. Don't forget radio, cell phone charging, etc. For the battery to last you must be able to put more juice into it from the solar panel than you use.
What's the ah capacity of the battery? Since you'll be out 2 weeks, you may get some clouds/rain, so based on usage how many days could you go without recharging?
I'll guess that you *might* be OK, but 2 weeks is a long time on one battery with only 50W solar...even without TV or furnace. You might consider a small generator just to give the give the battery a full charge a couple of nights and also to run the furnace if need be.
