I had residence in a foreign country for 284 days in 2017. My residence started in 2016 then ended in the middle of 2017. I went back to the US for about three months before coming back to the same foreign country and took up residence again.
Am I able/supposed to fill out the 2555-EZ (I did make less than $102,000 in total?) If so, how do I fill out the portion that asks for the dates of my residence since it wasn't continuous?
I assume you are not using the bona fide resident test, but rather the physical presence test.
(See 2555 instructions, https://www.irs.gov/pub/irs-pdf/i2555.pdf , page 3.)
To qualify under the physical presence test you need to have been in the foreign country for 330 days during any 12 months. Those 12 months must include some time in 2017. E.g. they can either begin or end (or both) in 2017. They do NOT all need be in 2017. E.g. 1/2/2016 to 1/1/2017 would qualify.
So when TT asks you for the dates it is fine to put a 2016 date for the beginning of the period as long as the ending date is in 2017.
You still have to meet the 330 days. See the instructions for what counts.