Mine has never had screen flicker. I don't know if the Tab S 10.5 suffers from that symptom.
Unlocked generally means it can be used with "foreign" sim cards, at least, in phones. For Verizon, again, with phones, that means it can be used in Europe on their gsm frequencies. In the US, I'm not sure and I really don't know if Verizon tablets are intended to be cdma in the US like their phones or if it may be more open.
You want a bill of sale and make sure that it is not a lost or stolen device.