Can I still submit medical expenses for 2018 taxes, within the 1 year period between July 2017 and July 2018, if I only become eligible to file in 2018?

You can choose any 12-month period for your medical expense claim as long as it ends in the tax year. So if you have medical expenses in late 2017, you can claim them in 2018, if that is the best period for you to claim.

Thanks. And there is no problem if I only become eligible in 2018 to submit taxes?