BISMARCK, N.D. — A constant stream of changes and scuffles are unsettling Donald J. Trump’s campaign team, including the abrupt dismissal this week of his national political director.

A sense of paranoia is growing among his campaign staff members, including some who have told associates they believe that their Trump Tower offices in New York may be bugged, according to three people briefed on the conversations.

And there is confusion among his donors, who want to give money to a “super PAC” supporting Mr. Trump, but have received conflicting signals from top aides about which one to support.

On Thursday, Mr. Trump secured the Republican Party’s nomination for president, a remarkable achievement for a political newcomer. But inside his campaign, the limits of his managerial style — reliant on his gut and built around his unpredictable personality — are vividly on display, according to interviews with nearly a dozen Republicans inside and outside of the operation.