Washington — Several questions are being asked here following President Reagan's dramatic meeting with Soviet Foreign Minister Andrei Gromyko, the first such high-level get-together during his presidency. Among them:
* If reelected, what is Mr. Reagan willing to offer Moscow in substantive terms to show he is serious about improving Soviet-US relations?
* Is the President prepared to make changes within his bureaucracy to resolve internal disputes and achieve consensus on an approach to arms control?
* Can the Soviet leadership, weakened by uncertainty about President Konstantin Chernenko's health, come to grips with the policy decisions required if the United States offers an attractive concession?
US diplomatic experts in and out of government are not surprised that last week's events at the UN and in Washington did not lead to substantive accords. Mr. Gromyko, it is felt, was basically on a reconnaissance mission. He was probing to see what lay behind Reagan's change of style and apparent flexibility , but did not wish to hand him anything that would boost his prospects for reelection.
But the 31/2 hour Gromyko-Reagan encounter is cautiously viewed as a net gain in terms of eventually improving US-Soviet relations. Experts say it is a good beginning. At the same time they warn that any progress is likely to be long and protracted, requiring patience on the part of the US public and no expectations of quick solutions or early breakthroughs.
''Gromyko can't come here and meet and shake hands without relieving some of the atmosphere and raising expectations on both sides,'' says William Hyland, a Soviet specialist and editor of Foreign Affairs magazine. ''I don't think much will happen until after November and even then until spring. But the Russians probably have opened the door to dealing with Reagan.''
Even some analysts who generally criticize the administration's handling of US-Soviet relations give the President credit for a deft display of diplomacy this past week. Granting that Reagan stands to gain politically from his present conciliatory posture, his recent moves point to a more nuanced approach to Moscow.
The first move was postponement of an administration report on alleged Soviet violations of nuclear arms agreements. Then, in his speech to the UN, the President said he was willing to consider some form of ''mutual restraint'' on the testing of antisatellite (ASAT) weapons if the Soviets agreed to space talks. Gromyko probed this issue with Reagan and Secretary of State George P. Shultz.
''The President has demonstrated genuine flexibility,'' says Dimitri Simes of the Carnegie Endowment for International Peace. ''This has been a useful process. It does not mean things will stay on course. But for the first time, the administration has done something right - being open-minded but not overeager.''
Administration officials are restrained but positive in their assessment of the Gromyko visit. They characterize the meetings between Mr. Shultz and the Soviet foreign minister that followed the White House get-together as constructive, useful, and providing a basis for easing tensions in the months ahead. The President is portrayed as having given a very forceful presentation in a two-hour exchange with Gromyko, during which their aides were present. He also is said to have led the conversation during a private eight-minute meeting with the Politburo member in the Oval Office, stressing his desire to put relations back on track.
''Now the Soviets will return home to ponder our exchanges,'' Reagan told the nation in his weekly radio address Saturday. They will get ''a fair deal'' if they negotiate, he promised.
As the two sides continue their exchanges, observers doubt that there is enough time before the election to start some form of negotiation. But many experts say the men in the Kremlin have come to the conclusion that Reagan will be reelected and, despite their positive tone toward Democratic challenger Walter Mondale, are laying the groundwork to do business with the Republican incumbent.
''The Russians are cautiously responding to new indications of a willingness on the American side, and they cannot afford not to explore it,'' says Mark Garrison, director of the Center for Foreign Policy Development at Brown University.
While the President appears to be serious about reaching agreements with Moscow and is now demonstrating more flexibility, say experts, he has yet to deal with the deep conflicts over arms control between the hard-liners in the Defense Department and more moderate elements at the State Department and in the White House. If the superpowers are to break the stalemate in arms talks, it is argued, Reagan himself will have to resolve the infighting and force a course of action.
''He has to give a clear signal of what he wants,'' says Helmut Sonnefeldt, a Soviet expert and former US diplomat. ''He'll have to push hard because there will be resistance in his own constituencies and in the Defense Department. He has to manage that in some fashion and find ways of persuading these people that he knows what he is doing and will not sell out to the Russians.''
In this regard, Reagan is given credit for deciding to meet with Gromyko - a move planned by the White House and State Department and kept secret from the Pentagon, according to press reports.
Since the first of the year, the President has adopted a more conciliatory stance, culminating in his UN speech, which did not mention his disagreements with Moscow, and his meeting with Gromyko, during which Reagan assured him that the US does not seek to change the Soviet system or the Soviet-backed order in Eastern Europe.
The road ahead is expected to be difficult, whoever is elected president. Shultz stressed that distrust, apprehension, and many differences of opinion remain. But administration and outside experts say some progress has been made.