It's hard to say what your heartrate at rest should be, as it varies from person to person. People who have excellent cardio fitness, for instance athletes etc can have a RHR of 40. The average person is between 70 and 85, but the lower the RHR, the more efficiently the heart is seen to be working.
People who have poor cardio fitness tend to be in the high 80's to 90's.
If you are exercising at a moderate intensity, say you are working at 65% of your maximum capacity, then your heartrate (for your age) should rise to around 111 Beats per minute. An indication of poor fitness levels, is when it rises much higher, especially during moderate activity. If you are a smoker, then your lung capacity would be affected more so than a non smoker.
Again recovery time is dependant on the individual. You would need to time your own recovery rate from when you stop exercises to when your heartrate returns to it's normal resting rate. Over the weeks, as you get fitter, this time should reduce, which is a good indication of your progress.