Ruth Davidson and Jacob Rees-Mogg will be two of the most visible politicians at the Conservative party’s annual conference, which is set to be dominated by leadership speculation, angst about how to win over young voters, and the shape of Brexit.

The MSP and MP, mooted as possible candidates to succeed Theresa May, are making a series of high-profile appearances at fringe events in the first week of October, with the Scottish Conservative leader giving two public interviews and speaking at two receptions.

Rees-Mogg, the rightwing backbencher who has been the subject of summer speculation over his leadership ambitions, is lined up for at least six fringe events focusing on the challenges of Brexit.

Cabinet ministers appear to be keeping a relatively low profile, with Boris Johnson scheduled to appear at just one event on “global Britain”.

The conference will be a key test of the feeling among activists toward May, but party sources said the mood among the grassroots and MPs was expected to be depressed after the disappointing election result.

One unwelcome guest for the prime minister will be the former chancellor George Osborne, who has been using his editorship of the Evening Standard to campaign against her Brexit strategy. He will appear at a fringe event about devolution and the “northern powerhouse”, after staying away last year in the aftermath of the referendum.

The party’s fringe guide and agenda, published this week, shows the Conservatives will spend most of their time wrestling over how to appeal to young people, and what went wrong at the election.

Justine Greening, the education secretary, and Sajid Javid, the communities secretary, will start the first day with a session on “delivering a fairer future for young people”, as concern grows within the party about the overriding appeal of the Labour leader, Jeremy Corbyn, to younger voters. Greening’s brief covers university tuition fees and Javid is responsible for housing policy, which were two issues Labour used to attract the votes of under-35s at the election.

The former cabinet minister Eric Pickles will present a report about problems with the party’s centralised election campaign. It will identify the party’s depleted activist base as a major problem and recommend ways to enthuse younger supporters.

In an interview with The House magazine, Robert Halfon, a former deputy chairman of the party, said on Wednesday that the party needed “radical, counter-intuitive revolution … if we are to survive”.

“If we don’t radically reform our messaging, our machinery; if we don’t focus on policies that really are there to help the lower paid, which are supported by people in metropolitan areas, I think, we’ll face a precipice. Corbyn will be in No 10,” he said.

Voters backed the party with “gritted teeth” and the Tories’ problem with young voters was massive, he said. But he cautioned against concluding that they supported Labour because of its pledge to scrap tuition fees.

“It isn’t just about money. I think if we make that mistake, we will make a big mistake as a party. I think young people are voting Labour because they believe that it is a noble thing to do,” he said.

“Who would not want to vote for a Labour party whose main mission is to help the underdog. I would love to do it, because why would you not want to do that?”