Shall we migrate directly from SP 2007 to O365 direct?
Yes, you can migrate directly from SharePoint 2007 to SharePoint Online, It's not like the SharePoint On-Prem where you should first upgrade to SharePoint 2010 to can upgrade to SharePoint 2013.
If yes, Could you please list out various options available to migrate to O365 directly?
What will be checkpoints need to be verified before start migration?
Does anyone already done this and can explain various pitfalls?
To be honest, I didn't try to migrate from SharePoint 2007 to SharePoint online to list the actual pitfalls that will differ from one environment to another (
I tried to migrate from SharePoint 2013 to SharePoint online with 3rd party tool and the result was great)
At the same time, I advise you to check and compare the missing and new features between SharePoint On-prem and Online. Also, check this article that shows the common pitfalls to Migrate SharePoint 2007 to Office 365.