Specific Matchup Comments:
D520 vs Bf109E: This is the most common matchup, because once the Bf109F comes out, the H81 is usually available as well. You have several disadvantages vs the Bf109E, and two advantages. The disadvantages are speed and climb, while your advantages are high speed rolling capability and turning ability. It is best to engage 109s with an altitude advantage, and failing that, get into a turnfight with them. If the 109 turns with you, smile, as you'll soon get on his six. Keep in mind that your rolling advantage applies to high-speed flight only, once slow, the 109E can roll just as good as you.
D520 vs Bf109F: The F model made the 109 much more dangerous. Now the plane has plenty of cannon ammo, climbs faster, flies a whopping 70kph faster on the deck, and turns better than the 109E. Use anti-109 tactics mentioned above, but be more careful, as the 109F can easily stick his nose in the sky and yoyo you to death.
D520 vs Fw190a5: Be very careful with this plane. It has a 115kph speed advantage over you on the deck, outclimbs you by a large margin under 3km, and can dive like a brick. Try to keep your fights above 3km, better yet, try not to fight these beasts at all. However, if you find a 190 down low and slow, smile, as the pilot probably doesn't know what he's doing, and will soon end up as a kill sticker on the side of your plane.
The D.520 remained in use after the Armistice. The German armistice commission allowed the Vichy air force to use the D.520 in Africa. The Germans even placed an order for 550 D.520s themselves (349 were produced between August 1941 and December 1942), using them as training aircraft. Some of these aircraft were sent to equip Vichy squadrons in Syria, where they saw action against the Allies in the summer of 1941. In this campaign the D.520 claimed 30 victories for the loss of 32 D.520s.
The D.520 had one last chance to fight the Germans after the Allied invasion of southern France in August 1944. Within days of the Allied landing the French Forces of the Interior formed a fighter group (Premier Groupe de Chasse FFI) which fought alongside the allies in southern France, using D.520s recaptured from the Germans, before being absorbed into the re-formed French Air Force on 1 December 1944. This fighter group used the D.520 from August 1944 to March 1945. By now the D.520 was effectively obsolete, but the Luftwaffe had been swept from the skies of southern France by Allied air power, and so the D.520 was able to play a role in the mopping up operations in south west France.