Grigory Romanov would probably have been chosen to succeed Chernenko. The Cold War would have continued, Soviet economic tinkering beginning in Andropov's time would continue (ie minor reforms and increasing efficiency rather than replacing the Stalinist economic model), Soviet involvement in Afghanistan would continue until they deemed that Afghan troops could handle the situation for themselves. I would expect that the anti-corruption campaign would continue, at least in name.
Economic growth rates would improve slowly, but ultimately not at the pace of the USSR's Western competitors, which would be troubling for the leadership. Nevertheless, the destruction that occurred throughout the Perestroika period would not occur, and people would be much more satisfied with stability than historically they were with economic flux and the noticable decline in the standard of living.
Furthermore, the lack of political reforms ala glasnost attempting to turn the USSR into a social democracy would prevent nationalists, capitalists, liberals and anyone else seeking to take political power away from the CPSU from ever organizing effectively. This would mean, among other things, that there would be no ethnic unrest, violence, and demands for independence on the scale seen in Gorbachev's time. Also, there would be no radical demands to reform the system along ideological lines away from Marxism-Leninism.
Soviet support for the socialist states of Eastern Europe would continue, making anti-socialist agitation efforts there impossible to succeed, and far more unlikely to ever begin (after all, many of the groups that historically agitated against their socialist governments began after Gorbachev's radical reformist path had been announced, and after he hinted at non-interventionism).
Overall, the big challenge for the leadership for the future would have been to find a way to reform the economy on socialist lines, that fit current demands and conditions better than the Stalinist economic model, which had been designed for radical industrialization, and not for consumer production and high-tech specialization of 'advanced socialism'. Plans for various problem areas did exist, small scale examples of success abounded in Eastern European countries and the USSR itself, and the USSR had trained some of the brightest and most creative scientists and mathematicians in human history. I'm sure that after a certain period of research these scientists would be able to find a way to peacefully and successfully shift Soviet economic production to a post-Stalinist model without compromising ideology.
Doubt that. Unless there was an anti-reformist direction in the CP the fall was inevitable
You have to remember that Gorbachev, as General Secretary, had the power to mould the Central Committee and the Politburo. Effectively, he used this tremendous power to remove his opponents, and to put in their place reformers and idealists who thought like him. The power of the General Secretary of the CPSU in this capacity is perhaps something to be critical of.