Regardless of what people may think of the controversial comments Donald Trump made during his presidential campaign, he has been a public figure who has negotiated international business deals for many years. He understands tact and working with others to accomplish mutually beneficial outcomes. He is already accepted as a leader by many other world leaders.
Trump is a lot of talk. In the end, Trump wants to run the country like a business. He doesn't want to destroy the United States or the world, because then the companies wouldn't make money. Trump knows that nuclear weapons would literally destroy the world. He would not use them lightly.
I really don't think Donald Trump takes anything seriously, unless it's his fortune. He is a completely inexperienced politician, who is already causing damage with his lack of tact in international relations. He needs to start listening to his advisers soon, before he goes too far and causes irreversible damage.
We already have enough nuclear weapons to blow up the Earth several times over, but yet he's making more? He is very impulsive and isn't a good choice making, which isn't exactly ideal when it comes to handling nuclear weapons. He can't even handle criticism, much less a nuclear arsenal. A country that would have no biases and usually stays out of war, such as Switzerland, needs to disarm every country on Earth of their nuclear weapons. Nuclear weapons are simply too destructive for anyone to use because they could create an apocalypse or destroy the earth entirely.
Nobody who fully understands the seriousness of nuclear weapons would advocate creating more, upending 30 years of foreign policy and potentially reviving the cold war.
He's suggested that the US withdraw military protection of Japan and South Korea if they don't "pay up", which would open the door to either of those countries legally constructing weapons of mass destruction, again upending decades of foreign policy and setting a dangerous precedent.
He didn't know what the Nuclear Triad was, and didn't bother to learn when it came up repeatedly. He has repeatedly asked why we can't use nuclear weapons if we have them. The president is a figurehead more than anything, and he doesn't seem to understand that the things he says, more than anything else over the course of his presidency, will dictate the path of this country moving forward.
No, Trump does not seem to appreciate the seriousness of nuclear weapons. He seems to brush off any questions about them that the media raises. He cavalierly suggests that we need more weapons and should just go and make them. Then, he goes and refuses national security briefings. None of his actions seem to indicate he takes nuclear weapons seriously.