In your css use
'.ui-datepicker{ z-index: 9999 !important;}'
Here 9999 can be replaced to whatever layer value you want your datepicker available.
Neither any code is to be commented nor adding 'position:relative;' css on input elements. Because increasing the z-index of input elements will have effect on all input type buttons, which may not be needed for some cases.
Lots of time I got opportunity to make a website for my friends and other persons but I always refused and rather I taught them “how to build a website” or blog.
This time it looks like I am going to make one for someone. Just registered a domain bdca.in and installed a script on it. Waiting for name sever propagation to complete and then I will try to finish it as soon as possible. Lets see how it comes out to be.