Do most of today's democratic nations with two-party system exhibit a civil war in recent past?

I'll answer only for the United States, the country I know best, but the answer is yes. That is, the Civil War shaped the two party system as it exists today.

Prior to the Civil War, there as a "crazy quilt" of parties. A 36 year period from 1824-1860 began with the ruling party as the "Democratic-Republican" Party. The main opposition party morphed from the Federalist party to the Whig Party. A third party, the Free Soil Party, arose with only a handful of Congressional seats, but held the balance of power between the two larger parties, which were initially closely matched. When the Whig Party collapsed, the Democratic-Republican party split into "Democrats" and "Republicans," with the remaining Whigs, and Free Soilers joining the newer "Republican" party. This "confusion" helped bring about the Civil War.

The American Civil War changed all that by dividing the country North and South. It also created a two party system, with the Republicans controlling the more populous northern states, and the Democrats dominant in the South. From 1860-1932, the Republicans dominated Presidential politics. Basically, the only Democrat that had a chance to win during that time was the governor of New York State. That's because if you added the "tri-state" area of New York,the most populous state, (plus New Jersey and Connecticut), to the old Confederacy and border states, they had more electoral votes than the old Union MINUS these. Democrat Grover Cleveland won two (split) Presidential terms this way, and Democrat Samuel Tilden lost by one electoral vote, getting most of the Confederacy PLUS New York, but MINUS Mississippi, South Carolina and Florida. (Democrat Woodrow Wilson (Governor of New Jersey) was initially elected President because of the split of the Republican party between Teddy Roosevelt and W H Taft.) It is noteworthy that Franklin Delano Roosevelt had been governor of New York, although he won a bunch of former Union, and newly created western, states, because of the Depression. It was only after FDR that both the Democrats and Republicans realigned, by which time memories of the Civil War had faded.

The U.S. has a two party system because of winner-take-all elections and the powerful executive branch. There are no run off elections so "third parties" are considered spoilers and can't gain traction.

I doubt this is to do with a civil war, but instead to do with the voting system. This is Duverger's law. The USA & the UK use a first past the post system, as opposed to a proportional representation system, and under that, the system tends to 2 parties.

The UK is in Europe, has had a civil war (though is irrelevant now), and has a 2 party system (sorta debatable now, since the Lib Dems did well). Ireland, has a PR system, and is quite culturally similar to UK, but nearly always has coalitions & multi parties.

The UK had a referendum recently on whether to change the voting sytem to a proportional representation system and voted no, so there won't be any change there for a while.

The people of the USA have a strong narrative of their country being great for democracy, and haven't really changed any fundamental parts of the voting system (giving blacks the vote was probably the last change). It can be hard for someone to seriously question something that they view as fundamentally good (i.e. maybe the USA voting system isn't the most democratic system there is).

There may not be enough data to get any meaningful answers, but it's worth remembering that the U.S. has had a two-party system for most of its history, including before the civil war (Federalists vs. Anti-Federalists, Federalists vs. Democratic-Republicans, Democrats vs. Whigs). As for other countries, remember that almost no country has a system as strong as that in the U.S. In Spain, for example, there are generally considered to be two major parties and many minor parties which sometimes join coalitions but almost never run the government. Spain did have a bloody civil war, but the two-party polarization arguably preceded this in the form of Republican/Monarchist strife which had existed since the Napoleonic Wars.

Also, several countries or political systems might be said to be developing or to have recently developed two-party systems without a civil war. Examples are Venezuela, where a once-broad slate of parties has become quite polarized along pro- or anti-Chavez lines, and the European Union, whose parliament is usually controlled by either the European People's Party or the Party for Socialism and Democracy. Although both World War II and the Cold War could be considered intra-European civil wars in this context, the ideological ancestors of the center-right and center-left are generally considered to have been on the same side in both these conflicts.

After looking at these examples I'm tempted to turn the question back to you: can you name a country whose two-party system is the result of a civil war?