I'm sure this can be discussed elsewhere, but wouldn't the FW-190 be underpowered with a DB-605? If we are talking about building something else instead of the Me-210/410, i'd have more Bf-109s instead of the Me-210 and the FW-190C instead of Me-410.
Anyway, back to possible Bf-109 production, how about Japan? Just like Italy, if they get the licence for 109E early enough, say 1938, it might make a difference especially for IJAAF as the poor sods were still flying the fixed gear Ki-27 in 1942! Not sure what the 109Es role will be in IJAAF and even IJNAF though, perhaps seen as a stopgap until the Ki-44 and Ki-61 and J2M respectively come online? Perhaps even displacing some of the types built in OTL? If say they get the licence for 109E and they built a good number by 1942, it will be a nasty surprise for the americans (who though they kept meeeting 109s anyway in OTL), the Bf-109E was generally superior to the P-40 not to mention Hurricane so no diving to escape here, while later on as the war will move against Japan the Bf-109F/G would be an excellent interceptor from 1943 onwards, certainly worth replacing the Ki-43 with in a defensive role, but how about the Ki-44, and Ki-61? Based on the specs, it certainly appears so too, especially when fitted with GM-1 it could be more effective against the B-29, though again the 109G does not have the range of the Ki-61 and Ki-43. For the IJAAF, replacing the J2M (and i say, even the N1K1-J as it was sadly a half-cooked fighter, the N1K2-J is good though) with the Bf-109F/G also seems like a good choice? Certainly, just like with Italy the 109 should be simpler to build than most if not all japanese fighters named above, so they could build a goodly number of them.