I think that many Republicans are convinced that Trump is qualified to be president of the United States. Many of his views, however outrageous or extreme they may seem, are in line with what a lot of Republicans want from the government in this upcoming term. He takes an extreme position on many issues, which is appealing to those who are against Hillary Clinton's campaign.
No, I do not think Republicans are convinced that Trump is qualified to be president because most of the GOP's leaders are still hesitant to fully endorse him and stand by what he says. Trump won the Republican primaries because the voters were mostly white, but he will surely fail to win the general election race.
A senator from Iowa made headlines when he announced that he would leave the Republican Party in an act of protest against the controversial presumptive nominee, Donald Trump. This is an indication that fewer and fewer Republicans believe that Trump has the qualifications to serve in the highest office in the land.
While many Republicans have voiced their support for Trump, many more have not. There a some that will not ever support him, and have publicly said so. Others are still considering the idea, without saying whether they support him or not. Even a few of those who have said they support him as the nominee are not totally convinced. I believe that very few people actually believe he is qualified, whether they will say so or not.