For the record, I've only used Nikons a few times but I don't imagine the most of the principles and realities are significantly different from those in Canon. Some of my answers are speculative but based on my experience with other cameras.
D5100 has 11 AF points and an older version of sensor. But how much does these points matter in practical life photography?
In some cases, fewer AF points can work more quickly though it can be at the cost of accuracy, particularly with moving subjects as of the 11 AF points, there's a single cross-type, which is faster and more accurate.
D7000 has semi weather proof body, internal AF motor, 39 AF points but no HDR mode. How to shoot HDR mode in D7000?
I'd imagine you just need to set your exposure bracket for an under-exposed, correctly-exposed and over-exposed shot. I'd be surprised if the D7000 doesn't have this.
Is the price difference between D5200 and D5100 justified for use of both in real life photography?
Only you can answer that but you'd need to be more specific on "real life photography". For what I shoot, the D5200's AF (on paper) alone would persuade me to buy it over the D5100 but since you said your photography will consist of slow or still subjects, you may not benefit enough from the D5200's AF advantage to warrant spending the extra money.
Any considerable difference in image quality?
As one succeeds the other, I think IQ differences are small in favourable lighting conditions if all else is equal but noise management in low light shooting may be improved in the D5200.
Does having a weather proof body and an internal AF motor in D7000 makes it a better contender than D5200 in real life condition? any considerable difference in image quality?
Again, you need to be specific about what "real life conditions" are. You could be on the Mediterranean coast of Turkey in the Summer where you're no better off having weather proofing than not but you could be in the Ardennes Forest being rained on constantly; both conditions are "real life" ones I've been in myself. If you're likely to be in rainy or dusty environments, the D7000 is at an advantage to it would be remiss not to have a rain/dust cover with either camera.
An internal AF motor makes the D7000 compatible with all AF lenses using the same mount, giving it a wider choice of lenses.
In most cases with contemporary DSLRs of the same sensor size, differences in IQ are far more apparent in the lens you use rather than in the body. Differences in IQ will probably be marginal though being newer, the D5200 may have less or at least less ungainly looking noise in low light.
...might even mount the cam on bike's fuel tank to shoot a video of speedometer.
It's obviously your money but are you sure you want to take such a risk? This sort of thing usually calls for using an action camera such as a GoPro. I'd imagine there are more options for mounting such cameras on your bike's fuel tank as well.