who is responsible for server monitoring ?
development team ?
Yes. They should be looking at the application server.
development team leader ?
Project manager ?
For database server, yes.
infrastructure team ?
Yes; overall server health. "Server" means the hardware and virtual machine on which the application server is deployed.
who is responsible when application
server is running slow or not
Depends on the root cause.
what tools are available for tomcat
Depends on where you want to apply them: aspects in apps, commercial monitoring tools if you mean the server, etc.