Obamacare
Those Obamacare statements do not actually conflict.
During the election, Donald Trump favored repeal and replacement with something better.
Trump thinks that preexisting conditions should be covered and that family members should be able to stay on the family healthcare until age 26.
Both those things can be true at the same time. While Obamacare made coverage for preexisting conditions and family members until age 26 mandatory, it's not required to support Obamacare to get those two provisions. They could be added in any replacement.
The single most important statement that he has made on Obamacare since the election was his selection of Representative Tom Price as Secretary of Health and Human Services (HHS). HHS oversees Obamacare (as well as Medicaid, Medicare, Social Security, and other services). Price is the author of one of the Republican Obamacare alternatives and is a big proponent of repeal. So the evidence is that Trump still favors repeal. If not, he picked the wrong head of HHS.
Prosecuting Clinton
I do not know of anything that he has said in explaining the different tone of those two statements. I wouldn't be surprised if he waited until after inauguration to address this further.
If I was going to pick a hypocritical thing that he has done in this area, it would be considering David Petraeus for Secretary of State. Petraeus obviously had his own legal problems related to classified information. But of course, that doesn't become really hypocritical unless Trump actually appoints Petraeus.
Building a wall
He still plans to build a wall. He may simply be switching from campaign rhetoric to actual plans. He acknowledged during the campaign that the wall was meant to augment existing obstacles. So there might be a section of wall, then a cliff face, then more wall. Since the election, he's also acknowledged that some parts of the wall might be built with fencing.
There is a general perception among his supporters that a wall is more of an idea than a physical barrier. For example, some have said that they would consider more border patrol agents to contribute to a "wall" with Mexico.
I personally expect Trump to finish the existing fencing plans halted under Obama. That plan already exists. What additional work he'd do remains unclear.
Climate change
Trump met with Al Gore and told the New York Times that he'd keep an "open mind".
Reuters:
"I had a lengthy and very productive session with the president-elect," said Gore, who met earlier with Trump's daughter, Ivanka Trump, but said he had spent the bulk of his time with Trump. "It was a sincere search for areas of common ground. ... I found it an extremely interesting conversation and, to be continued."
Gore did not say that they found common ground, just that they sincerely searched for it. Trump did not say that he no longer thinks climate change is a hoax. Perhaps Trump will reverse himself on this issue in the future, but he hasn't so far.
There is some evidence that Ivanka Trump is more inclined to environmentalism than her father. So this might be better viewed as Ivanka having different views. She set a meeting with Gore. She added her father to the meeting. Her father talked politely, as he often does in personal meetings (he's ruder on TV).
