Can we use metadata format (src folder) with vscode, if yes than how?
You can, but that means dealing with a package.xml and stuff that you've been dealing with, and using terminal commands or writing your own extension(s). VS Code is an IDE, but depends on SFDX for its commands, which do not all have an GUI option yet. So, you could develop in src, but you'd have to:
sfdx force:mdapi:deploy -d src -e true -l RunLocalTests
See the online help for additional options and preferences you can use.
Would migrating to source format will have any effect on our existing packaging org, also
No. Your components in the packaging org would remain the same as far as your managed package is concerned. You need to migrate to source format if you want to use VS Code GUI commands.
With eclipse IDE we have ZIP editor plugin added, by help of it we can edit JS files which are in static resource, Is there any similar tool available with VScode.
In source format, static resource ZIPs are automatically expanded on your local computer and zipped upon using force:source:deploy or force:source:push. There's no need for any extra extensions aside from the Salesforce Extensions Bundle.
Performance wise is it better than eclipse force.com IDE?
The performance is best when you use source format (mdapi tends to be far slower than force:source:deploy/force:source:push), and you can optimize your repository into packages/versions. If you can use force:source commands, you'll get far better performance than Force.com IDE or any other non-DX-based IDE.