What do you mean by "modern"?

As for the Su-27 itself, its only air combat experience comes during the Eritrean–Ethiopian War. Ethopian Su-27s fought against Eritrean MiG-29s. The former had Russian mercenary and some government support, the latter Russian and Ukrainian.

For the actual details, I am relied on an ACIG report on the war. I know ACIG was getting some flak in the TOP GUN thread, and it's not the best source, especially as this one has quite a few in built contradictions, but it's the only real one I've seen about the air war.

In brief, 5 MiG-29s were destroyed or damaged beyond repair for the loss of no Su-27s. This is despite the fact that almost no (1/24) R-27 radar guided missiles were successful and so the combat was mostly dogfights where the MiG-29 was supposed to excel. Again however there are contradictions, like the story of a female Ethiopian shooting down a MiG, but then other reports that the first female Ethiopian fighter pilot was years after the war.

Tons. The equivalent of the SU-27 is the F-15, which has seen lots of air-to-air combat, especially in Iraq through the 1990s and early 2000s. For the Su-27 specifically they engaged, and shot down, a handful of Mig-29s during the Ehtiopian-Eritrean war.

Edit: fixed a typo.