When you uninstall Office 2007 it will only remove the application files - it won't touch your documents. They'll still be there after the uninstall.
Office 2016 and/or 365 will be able to open the old file types without a hitch
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However... what I would suggest is that you make backups. It sounds like you may not have a backup plan in place, and I can't stress enough how important this is. A 16GB USB drive is less than $10 and would mean you can make a backup of all your important documents, etc. An external hard drive is even better, as you can make images of your existing setup - allowing you to roll back to a previous date if a problem happens. A little off-topic, but I thought it was worth mentioning.