To use support, raise an issue at https://support.atlassian.com
The maintenance service also includes the right to upgrade to any version of JIRA that's released before the end of your maintenance.
Patching is separate - patches are released as necessary and you don't need to be supported to use them. My understanding is that patching is not going to be done ad-hoc any more (where you replace files), it will be full installable updates.
Correct. As a quick example, if you have maintenance up to 5th November this year, and Atlassian release Jira 6.4 tomorrow, and 6.5 on the 6th November, you can upgrade to 6.4 any time you want to - on release, next year, entirely up to you. But you can NOT upgrade to 6.5 without renewing the maintenance.
You are suppose to be able to upgrade on an expired license to the last version that was valid for your license, but there could be issues where you might need to restore your data as noted in the JIRA Agile (Greenhopper) knowledge base article.
https://confluence.atlassian.com/display/JIRA/Updating+your+JIRA+License+Details (Read the comments section)
Even applying a new license after a license expired could be painful as well.
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