I am not much aware about the details as to which web servers support Web services written in Java.
Would Like to know the following three things:
1) What is required to have support for Web Services : Only Servlet Container or An Application Server + Web container?
2) Would like to know that do all Web Server supporting web development in Java support Web Services?
3) How to identify whether a particular server supports Web Services or not?
Thanking you in advance.
Your question is somewhat unclear. The term web service is applied to anything from a REST style API to SOAP based services to JSON based, etc etc. Wikipedia says an equivalent is a Web API, and an API can be pretty much anything.
So to answer your question. A servlet container is enough to support most common types of web services, it doesn’t require an application server. Take a look at Apache CXF, which is a framework catering for a lot of web services styles (notably SOAP and REST).
Apache CXF is a rather large framework, and can take some time to get your head around. If you need something simpler, you may be better off looking at some object serialization frameworks and implement the servlets yourself (this is what I do mostly). To serialize to XML, use out-of-the box Java JAXB annotations. To serialize to JSON, use Jackson.