The first question was answered on another page.
As for your second question, you are unfortunately not correct.
We can check each possible answer by adding up the costs for each road. I recommend getting a marker out to trace the path, to help keep track of which roads were taken.
So we have...
- Circuit ABDCA will cost AB+BD+DC+CA = 220+210+230+240= 900 in total (not 890). We can rule out choice A because the 890 and 900 don't match up.
- Circuit ACDBA will cost AC+CD+DB+BA = 240+230+210+220 = 900 in total
- Circuit ABCDA will cost AB+BC+CD+DA = 220+200+230+310 = 960 in total
We see that Circuit ACDBA is the cheaper route of the answer choices given, and it perfectly matches with choice 2.
This may or may not be the cheapest route. I'm not all that familiar with the Nearest Neighbor algorithm to properly find the cheapest route (the next best thing is brute force). Luckily we can just use the answer choices as shown above. Besides the question doesn't ask for the absolute cheapest, but instead, "one of the cheapest".
So once again, the answer for the second question is choice 2