RIP my karma, but I'll have a go.
Do you feel it's reasonable for him to suggest a policy like barring Muslims from entering the United States? If so, what is your take on the constitutional, ethical, and practical complications, as well as the effect on the US's image in other countries, in the event of such a policy?
I put the security of citizens above any humanitarian considerations. It might sound harsh, but the government, in my opinion, has a greater duty to protect it's citizens then citizens of other countries. Because Muslims both have a significantly high likelihood of being radical, and those who settle in the USA have a 30% chance of supporting ISIS/extremism, allowing ANY immigration poses a threat to citizens. I understand that humanitarian concerns are legitimate, however I place security of citizens higher on the significance ladder. There is no way to be absolutely sure any muslim coming into the country is not a radical, so for the time being I stand with Trump on this issue. You might say that many of the shootings were Whites, americans, etc. but in America they will not revoke citizenship, but preventing it/preventing people from coming is possible. The USA owes nothing to non-citizens, anything they give is out of benevolence.
How about his plan to somehow force Mexico to build a wall on the American border? Does that actually seem at all realistic to you?
To me, this is more of a symbolic thing/a grand suggestion that likely isn't serious. It does show that he is willing to engage on one of the most contentious issues facing the US today, the millions of illegal Mexican immigrants. I am all for legal immigration, but against illegal immigration. Trump is the one candidate who is willing to take any sort of stand on this problem that speaks to the majority of American's views - that illegal immigrants should be kicked out.
How about his various bizarre claims? Like vaccines cause autism?
While I don't believe that vaccines cause autism, if you read the scientific literature on the topic (I had to as part of a class I took), you will find that there is a lot of uncertainty, manufactured or otherwise, surrounding this issue. There are studies that claim a link between the two, and studies that disprove this link - so which study you think is true really comes down to which one you believe in.
Or that London is so radicalized that police are afraid to go on patrol lest they be murdered by Islamic terrorists?
I will not deny that Trump likes to exaggerate. However, 30% of UK muslims believe ISIS' actions are justified. So take that as you will, personally I can see how there would be fear given that such a high percentage support ISIS, suggesting they might also be willing to carry out such actions.
Or that global warming is a hoax?
I believe you are referring to a tweet Trump sent here: https://twitter.com/realdonaldtrump/status/418542137899491328?lang=en
While personally I believe global warming is real and threatening, I also see where Trump is coming from. Changing the world economy because of global warming when the market is not forcing/requiring it is a tall order, and I think Trump is one of those "It won't affect me/it is so far off/the world has gone through changes for millions of years..." types. I don't necessarily agree with all his policies, but I am willing to forgive some because others I do agree with.