You are referring to Italy
I live in a country,
There are bridges and rivers and boats,
A reference to Venice- a city that only uses boats as a means of transport...
on the axis.
In WW2 Italy fought on the Axis' side.
There was fighting over a roulette, tourists wandered throughout its capital
In the first half you are referring to Colosseum as Roullete means a 'wheel' and the shape of the Colosseum is circular. I also thought that it might have been Casino as Casino is a word of Italin origin but the Op said my first answer was correct. In the second part you are referring to Rome, sounds like roam (roam is a synonym of wander) which is also its capital.
Askew was the roller pin,
The leaning tower of Pisa.
copy and paste on the tomato sauce.
This is referring to Italian coffee and pasta, famous Italian cuisine.
The circle constantly snoozes,
Op says this is referring to Pizza. Circle is a clue to Pi and snoozes to zz.
pelicans on a city.
This is referring to Vatican city I am sure. The hint is that Pelican rhymes with Vatican.