Both questions drive at two big problems in this entrenched crisis. The first is the danger that debt-burdened countries are picked off by the markets one by one because they lack financial clout. And the second is banks which have got themselves into debt trouble because they lack a policeman in a border-free continental market.
And both questions touch on jealously guarded areas of national sovereignty and the power of the financial industry.
In reality, the differences between the bloc's three biggest hitters, German Chancellor Angela Merkel, French President Francois Hollande and British Prime Minister David Cameron are not huge.
In contrast, for each of them the risk of loss of face is big, which will make a compromise so much more difficult. The meeting will be a high-wire act for all, and the bond markets will offer no safety net.
Merkel, who leads Europe's most powerful and one of its most fiscally disciplined economies, is under pressure to be flexible towards financial bailout mechanisms.
As the main contributor to its rescue funds, Merkel has staked political capital in her opposition to any sharing of eurozone debt. To a lesser degree, she also resists new borrowing by the eurozone to finance growth, suspecting this to be yet another bogus alternative to belt-tightening.
But Merkel is now under pressure.
Business confidence in Germany is at its lowest level in more than two years, for growth across the euro region, the biggest source of exports for German firms, is weakening as austerity measures curb demand.
"With the German economy slowing rapidly and investors starting to question the safety of German debt, it is possible the country will change course. But at present it appears that Germany is not for turning," notes Simon Tilford, chief economist at the Centre for European Reform in London.
Since his election in May, Francois Hollande has rallied more and more opinion in Europe to his campaign for growth measures that include using European Investment Bank (EIB) loans and unspent EU regional funds to pump money into infrastructure programmes.
But cracks are beginning to show in Hollande's own position. France's borrowings last year rose by €100 billion ($159 billion), reaching a record 90 per cent of GDP. After promising voters he would support jobs, he is now having to contemplate deep cuts in government budgets to keep France within the eurozone's tougher rules on spending.
Ignazio Angeloni of Bruegel, a think-tank in Brussels, fears these major economic powers are playing a perilous game of "chicken".
"Negotiations are slower than one would hope because each side is using delaying tactics to obtain maximum concessions from the others. The two main players, Germany and France, differ in that the second can accept further EU federalism only if it [first] sees effective crisis resolution instruments in place, while the first is prepared to accept the latter only after having secured the former," he said.
Nicolaus Heinen, an analyst with Deutsche Bank Research in Frankfurt, predicts the summit will be a test of exactly how far Merkel and Hollande can push their own agendas.
"Hollande has a strong political backing in France. However, French ideas on setting back reform efforts and increasing consumption will be limited by the limited willingness of capital markets to finances such adventures," he told the Herald. It will be a test "but they will pass it as both sides are fully aware now what is at stake", predicts Heinen.
While all EU leaders agree on the need that fundamental reforms be introduced if the bloc is to become more resilient there are different views on exactly how to enforce the rules.
"The present 'rules-based regime' has not worked well because political leaders either change the rules when they become inconvenient ... or ignore them without penalty," Erik Nielson, global chief economist at Unicredit Research in London, wrote in an analysis. "At the other extreme, it is not clear that a fully fledged political union as in the US, with a directly elected president and central government, is needed either."
Britain is outside the single currency, but the continent's economies are vital for British firms. Prime Minister David Cameron will be under pressure to back the rescue operation for the euro but he must also avoid stirring up the powerful faction of europhobes in his own Conservative Party. And he will also scrutinise any plans that could weaken Britain's dominance in the banking sector.
"I think the eurozone will move to create a common banking community, or a union under a single authority, which will take power over the banks just as in the 1950s, when steel and coal industries were put under common authority," predicts British Labour MP and former Europe minister Denis MacShane.
"This will guarantee that no citizens will loses their savings [in a bank collapse] but it will mean that bad banks get shut down," he said.
For the City of London, which would remain outside such a jurisdiction, "it will be a big challenge."
