On my return trip from Fla., these 2 lights started to "blink" and now are running constant at high rpm?

Is this an "bad oxygen sender" light and if so, why the battery light "on" also?

My generic oxygen sensor is only 1-2 years old, is it normal to have to replace so often?

PS.  My 1.9l gas engine does not have a catalytic converter as I'm in a non-emission's county.
Can I run my engine w/o an oxygen sensor and ignore the lights?  If so, what harm would that do?

Thanks for info.

Larry
Ga.