I can answer the part concerning the shutter lag, this is something I used to think my camera (Nikon D300) suffered from before learning why and how to overcome it.
When you push the shutter button there are two stages, the first stage being to activate the autofocus and the second stage actually firing the shutter. If the camera has problems focusing on a subject due to low light, rapid movement or complex scene, then it can take an extra period of time for the camera to confirm focus before it can then go to the second stage and fire the shutter.
There are two ways to overcome this issue ... firstly you can pre-focus by holding the shutter button half way down and hence giving it time to focus before you need the shutter to fire. The problem with this option is it does not allow for moving subjects as well and it can be tricky holding the button half way down to activate the focus early.
The second option is the most often used and certainly produces the best results, this is to separate the focus activation and the shutter activation on to two different buttons. This enables you to have one finger on a button that activates the focus and can keep it running while your normal shutter button is on another finger and can be fired at anytime. Now if you combine this with changing the focus mode to be continuos focusing and possibly utilize a single point of focus, then you have a system that can track a moving object very well by holding down the button dedicated to focus activation and then firing the shutter via the normal shutter button at anytime or multiple times for an instant in focus sharp picture.
On my D300 the focus activation is moved to the AF-ON button allowing me to activate this with my right thumb while simultaneously firing the shutter button with my right index finger whenever I wish and as often as I wish.