Question About Old Recumbent Bike I Use, Please Help!

First off, assuming you don't pedal like a lazy walk, you'll burn 1000kcal in 2 hours, yes. That's roughly 125w average, which even on a recumbant should be manageable for most any male, even a smaller height guy like yourself.

Unless you have crazy aerobic fitness I don't know about, I'd say the absolute worst case scenario if you're giving it a solid cardiovascular effort is about 900 kcal in 2 hours, with as high as maybe 1300 kcal being possible. Doubt you'd be higher starting off unless you have some good cycling/running background fitness.

FYI: The mph on the screen is worthless. It has no bearing on real life, in either direction faster or slower. If you're bike gave a power output in watts that would be meaningful, but on an indoor bike all other values are meaningless, except as an indication to whether you're going harder/easier than your previous rides.

Stationary bikes (recumbent stationary bikes in particular) have the potential to have reasonably accurate calorie calculators--better than just about any other equipment. Quite simply, this is because you neither have to support your weight or put and keep it in motion. A stationary bike doesn't need to know your weight, age, gender, or even fitness level to estimate how much energy it took to move the pedals. The amount of energy necessary to turn the pedals is the same regardless of who is doing the pedaling. A fit person might have barely broken a sweat while an out of shape person might be ready to pass out, but the amount of energy needed to move the pedals is the same. If the bike can't give a anything other than a crude estimate, if resistance isn't considered, then you might fall back on estimating "light effort," "moderate effort," and "vigorous effort". Those are highly subjective based on fitness level.

"Stationary bikes are in their own class of cardio machines because they support your body weight, Olson says. "If the bike is calculating calories based on technical data such as METs (metabolic equivalents) and watts (which measures power output), the calorie readout can be very accurate." In fact, researchers at the University of California at San Francisco's Human Performance Center found stationary bikes to be the most accurate of all cardio machines, with an overestimation of only seven percent."

Source: http://www.shape.com/fitness/cardio/how-inaccurate-are-calorie-counters-gym/slide/4