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i think servlet-api should not be add as a external jar file. it requires server to run. so you should configure server instead of add as a external jar.

you have to configure the class path for servlet-api also in the environment variable only then it can be compile and run

there is jar file available for connectivity if you are failed to find it then search for a zip file there are files containing jar files on official site

eclipse basic requirement is to provide jvm i.e jre or jdk depends your requirement.
eclipse and netbeans are ide. both provide you a environment to write a code easily.

better you download the jar file and add it in library instead of zip file

if you installed the jdk sucessfully then the only thing is left is to set the environment variable.

there might be only class files in a jar file and class files can't open in eclipse