Thanks so much for the explanation.
What I am confused of is the f number. A lens like the 18-105 has f/3.5-5.6. So the wider aperture is 3.5 without any zoom and can stop to f/22 (with full zoom it ranges from f/5.6-36). To say the AF point is till f/5.6 or f/8 ,and with D5100 and D5300 that is only for the central point, is somewhat confusing.
No. The cameras always focuses wide open (widest aperture possible) when speaking Viewfinder mode. With all the points.
Does this have any relation with telling the AF sensitivity is -3 EV for all points in D7200 (and -1 EV for central point in D5300)?
Actually yes. The f:number limitation is just the aperture, where the light hitting the AF-sensor starts being less - it's not an absolute limit for the ability to auto focus. The sensitivity describes, when available light is too small, even with an aperture at f:5.6.
What is the range of f/number meant to allow AF?
Again - every lenses focuses with their widest aperture - the AF- sensor specifications allows that to be wider than or equal to f:5.6. The f:8 specification was a result of the D7100 central point being one stop more sensitive.
Does this f/number thing restricted to central point in all cameras? Or the higher lines than the D5xxx not restricted to the central point?
No. The f:5.6 refers to all consumer cameras for all their focus points. Some cameras have points (central, normally) with higher sensitivity, allowing to focus lenses with smaller max. aperture than f:5.6 - if light conditions are well - using those points. That's the case with the D7100 and D7200
I am concerned with this as I like to have a reliable AF system. I am not a pro but I find difficulty to adjust focus in low light even with the AF illuminator On in my D5300 if the distance with subject is more than 2.5 meters approx. I have a chance for change and thinking of D7200 or D750. The other option is to keep the D5300 and get better lenses. I am asking if this issue of AF sensitivity and accuracy can be a decision-making and worth the change for now? And if having D750 is a great improvement in the AF that worth the full frame shift?
That's of course personally (the bolded) - and may be a matter of ones primary or casual needed works (or wants

).
The AF-systems of the D7200 and/or the D750 are better than the one of the D5300 - that's for sure - and this is not automatically helped by better lenses
Lenses with bigger max. apertures is good for low light situations - yes - but - It doesn't help you for focusing, though - because your focus system does not use the wider apertures - putting a f:1.8 lens on your camera makes no difference to the AF-system
You could try:
Using LiveView, set the lens wide open for focusing - and then change the aperture for a desired value before shooting. In that case, "better" lenses can be a help.
BirgerH.