Europe took a step towards post-virus normality on Friday when restaurants in Germany and Austria reopened for the first time in two months, and other countries loosened travel restrictions and threw open borders.

Berlin’s restaurants, cafes and snack kiosks were allowed to serve customers again, so long as they obeyed physical distancing. People from two separate households could share a table, but had to keep a distance of 1.5m from each other.

Under new rules, waiting staff are required to wear face coverings. Cooks and other kitchen staff are not. Diners are also recommended to wear masks, but these are not compulsory – unless you use the toilet. Buffets are banned and food has to be cooked on the premises.

While guests are not obliged to make reservations, Berlin’s senate has strongly advised restaurants to take down contact details of their customers, and to keep them for four weeks, in order to enable tracing in case of an infection.

The likelihood is that restaurateurs in the German capital will soon be allowed to put chairs and tables in front of their establishments without having to gain the necessary permit – on condition that the pavement is wide enough. Berlin pubs and shisha bars remain shut.

Austrian restaurants, cafes, bars, churches and some museums also reopened on Friday, with similar rules on face masks and physical distancing. The country has outlined plans for cultural events to resume next month – with 100 people permitted at first, and 1,000 from August.

Vienna and Berlin offer a possible route map for other European countries, including France, which is considering reopening its restaurants on 2 June. One district in the German capital, Friedrichshain-Kreuzberg, plans to ban traffic on Fridays and weekends, allowing restaurants to take over some streets.

As infection rates flatten, travelling across the continent’s borders is becoming progressively easier. On Friday, Slovenia proclaimed an end to its coronavirus epidemic. EU citizens can now enter freely, but non-EU travellers have to go through quarantine.

Italy is to allow travel within separate regions from 18 May and is set to dispense with all national travel restrictions from 3 June.

Germany has dropped a two-week quarantine requirement imposed in March for passengers arriving from other EU states. Britain, Iceland, Norway, Liechtenstein and Switzerland are all included in the new arrangement. German officials, however, said that quarantine measures will be reimposed if the infection rate rises elsewhere.

Germany’s public health advisory body, the Robert Koch Institute, said it will monitor other countries even more closely than it has been doing, in order to be aware of danger areas. The current R infection rate is 0.88 – with every infected German giving the virus to fewer than one other person.

It looks increasingly possible that EU citizens will be allowed to fly abroad this summer on holiday. Germany’s foreign minister, Heiko Maas, is due to hold talks on Monday with European counterparts from popular tourist destinations including Spain, Italy and Greece.

The Baltic states of Lithuania, Latvia and Estonia have opened their borders to each other to create a “mini Schengen area”. Free movement of people will be restored to all 6 million permanent residents of the Baltic states, but arrivals from outside the three countries will have to undergo a two-week quarantine period.

The easing of lockdowns is in response to sinking national death rates. Denmark reported zero deaths on Friday for the first time since March, while Spain said its rate was falling. The Spanish health ministry announced 138 fatalities, bringing the total to 27,459.

In Madrid, the government hailed large-scale population testing as a key tool in the fight against the coronavirus. It has warned that any premature relaxation of restrictions could have “enormous consequences”, given that only 5% of Spaniards have had the disease.

In an interview with the Guardian, Pedro Duque, a former astronaut who serves as Spain’s science minister, said that the preliminary results of a nationwide serological study published earlier this week would be crucial to the government’s response.

The study, which involved more than 60,000 people, revealed that around 5% of the population - some two million people - has had the coronavirus. It also showed that 33% of those who had caught the virus had not shown any symptoms.

“We think that the seroprevalence test we’ve carried out is the best that’s been done anywhere in the world so far. The most important conclusion we’ve reached is that it is vital to keep acting very prudently when it comes to this illness. There are still a lot of people who haven’t been exposed to the virus,” he said.

He added: “The consequences of acting irresponsibly could be enormous given that we know that only 5% of the population has some degree of immunity against the virus. That means that 95% don’t.”

Duque also dismissed talk of so-called “immunity passports” to allow more freedom of movement to those who have recovered from the disease. The science, he said, simply did not support such a move.

“From a personal scientific point of view, all I can say is that we don’t even know for sure that immunity exists, so we’re very far from all of that. We don’t have scientific information that guarantees that people with the antibodies are immune to future infections.”