Sinus pressure is lifting so I can tackle the first question.
I think the viewpoint of conservatives has to do with
Elitist behavior and opinions as opposed, to 'brick and mortar' wealth.
Trump has been described as a Blue-Collar Billionaire by his crowd. Started with a loan/gift from his father. Had understanding of the building-construction process which eventually evolved into business/real estate development. Respecting his employees, from the guy laying the bricks, to the doorman, to the head architect on his latest project.
There are many anecdotes of him shaking every hand of every employee in a restaurant. If he was in Mar-A-Lago on business and there happened to be Wedding in one of the ballrooms he would make it a point to stop by and meet the bride-groom and shake the parents hands.
This was a question posed in the general section of Reddit last month (not exactly friendly territory for Trumpers, outside of the r/The_Donald subreddit) Interesting read where you get a feel with how Trump interacts with Joe Blow.
People who have met or dealt with Donald Trump in person prior to the race, what was he like?
For a man of considerable wealth, he has done some over-the-top marketing of his brand. Trump "The Game", Trump Steaks, Trump Vodka, buying gold furniture and shit. He was a private citizen. Tends to gloat. However, there are many instances of generosity that he does under the radar. Lends out his plane to get Desert Storm troops home for the Holidays. Transport an ill child that needed special breathing equipment on board.
Trump and Obama both love to golf. Plenty instances of taking celebrities, athletes out. Trump and Brady. Both guys and Tiger. I'd be pulling that card too if I were President.
Onto the perception of Obama. I've stated that I think he will be remembered as a bad President. However, if had to pick an entourage of 4 Presidents to join me for a guys night out, he would be one of my top choices. Give me Obama, Clinton, JFK, And Teddy Roosevelt. I gather he loves to drink, watch sports, knows current pop culture. He stated back in 07' his favorite TV show was Entourage which I loved at the time. Seems like a fun guy and his ability to relate to people helped him in both elections.
In Presidential practice, conservatives have complained about his elitist behavior. Aloof attitude. Way back he had his Deplorable moment when he referred to those in Middle America as bitter people who clinged to their guns and religion during a closed door Fundraiser in San Francisco. That was the root of the claims of his Cosmopolitan Elitism all the way back in 2008. Broadbrush statement, that is probably rooted in some truth, but every clinger must be judged on their own attitude.
There were moments when Obama seemed to really want to stick it to the American people. It was an elitist move to shut down the WWII memorial during the government shutdown. The memorial itself is an open-air charity funded monument in Washington. Maybe it was his 'Art of the Deal' to end the shutdown. But the ones hurt the most were veterans (some of them dying) who arranged to take group flights to DC to see the memorial. For me that was one of his lowest moments of smug elitism.
Other conservatives argue his narcissistic elitism is on display almost every time he gives a speech or press conference. Refers to himself as "I" in some deliveries more than 200 times. Those are a couple reasons why conservatives view Obama as elitist. The super-haters can cite many more, I'm not super hard on him (just a few moments). Every President will have those tone-deaf elite moments. Bush 41 in the supermarket check out line. Bill parsing the word "is". Trump is bound to have his moments too.