Assuming the sexual preferences matched.
No, because you’re the last person on earth.
Are you okay?
Not if there were batteries still available. 
How tall are you? I don’t date short guys.
If you’re the last person, who am I in this scenario?
I think the concept of dating would lose some of it’s meaning in that sort of situation. Dating, in some cases at least, implies those doing so won’t also be dating others. It there are no others the concept seems like it wouldn’t apply in the same way it currently does.
Only for the purpose of making the second last person on earth jealous.
Depends, How often do you shower?
Which of us is paying for dinner in this scenario?
Two humans is not enough genetic diversity to propagate the species without serious genetic flaws manifesting, so reproduction would be right out, but as I hate babies and have absolutely zero paternal instincts, not a problem
Assuming you were female and weren’t looking to reproduce? Sure, why not…
Using carbon-14 methods, sure.
How did a goat log onto the internet?
Call me, maybe!
You remember that sequence in The Martian Chronicles miniseries? Where the last man on Mars found there was a last woman on Mars, and he was so lonely that he drove hours to find her. And she was totally obnoxious and unlikable, and he ran far away across Mars rather than spend one more minute with her?
Probably like that.
Doesn’t matter. There’s nobody working at the restaurant.
What brings on the question?
As long as you have a vagina its within the realm of possibilities.
But just in case ------ are all the sheep gone as well in this hypothetical?
You’re in Taiwan, I’m in Idaho. If we two were (suddenly) the last people on earth I would never never even get the chance to meet you, due to that whole “oceans in the way; no running planes” thing that would be going on. I probably wouldn’t even know you existed!
If we did somehow meet, I would probably deign to interact with you, out of desperation for human interaction if nothing else. At that point the way it would go would depend on you to some degree. For example if you were extremely rude, or you promptly murdered me, I would not date you. I do have standards.
Assuming neither of us alienated the other, and that we chose to continue to interact, I suspect that odds are good that I would start to feel affection for you. If you detectably returned that affection, and did not overtly express refusal of the idea, we would probably start dating, eventually.
Well, give or take that we’d have almost certainly starved to death first. I ain’t the foraging type.
Yes, but I’m not ready to be exclusive.
Regards,
Shodan