I recommend to step in some major versions before reaching the latest version like going to 4, 5 and then 6.4 version for safety reasons. Also, always perform a backup before any upgrade or change and between upgrades to create some check points.
Yes. Please read https://confluence.atlassian.com/display/JIRA/Upgrading+JIRA to get started with.
You WILL need to step through more than one version - I'd suggest 3.6 -> 3.11, then 4.4 then 5.2 then 6.3, but you must test that for your own system and adjust it if you need to
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