Following are the answers to your question, hope this will help some one.
Whether in cross platform if it is possible to achieve all the native
behavior of all phone models, something like in Android menu and
iPhone gestures?
No it will not supprot all the native featrues using Phonegap the look and feel remains like web. If you go for titaniam (I have done for one project) some features we need to write cusotm native code to achieve it. If you are doing this you have to do for both platforms iPhone an Android. Also the Titaniam will generate a lot of native code. So, my suggestion is either go to Native or go to Phonegap.
Apart from cross-platform advantage, what are other advantage do it
have?
Apart from cross-platfrom the main advantage is the custom controls, for example if you are doing a custom tab bar that looks different than the native it will be hard to do in native you have to write more code for that. In Phonegap as it is web you an do what you want.
What are the disadvantages? Is there any limitation when it comes to
comparing to native app?
As I told before, the UI will look like a web UI and some important features cannot be achieved. See this SO link for more information
Whether I can use same code without any modification in all the
devices or i have to change the code with respective to device
identified dynamically?
Yes you can do, but I have not done this yet. See this link some code change should be done with respect to the device type.
I hope this will help some one