Does anyone encounter these problems? Are the flight models realistic?
Remember that the late Bf-109G and the Bf-109K series represent the ultimate evolution of an airframe which was designed in 1934, while the La-5 and La-7 represent the ultimate evolution of an airframe designed in 1939-1940. The difference in "generation" is a big deal since the Bf-109G and -K series had to make sacrifices in order to incorporate bigger guns and a more powerful engine, while the La-5 and La-7 represented the peak evolution of a design which dated back to the LaGG-1 and LaGG-3.
Additionally, the La-5/-7 series were designed as short-range, low altitude air superiority fighters while most of the Bf-109G and K series were designed as high altitude bomber interceptors. Different roles, different strengths and weaknesses.
So, if you're flying a late war Bf-109, you're flying an old airframe design where maneuverability (and some other stuff) has been sacrificed for speed, armament, and, sometimes, high altitude performance. If you're flying a La-5 or La-7 you're flying a slightly less old airframe design finally combined with a decent engine and with the most severe drawbacks of the LaGG-1 and LaGG-3 "mostly" fixed. Additionally, the serious drawbacks of the La-5/La-7 series (like cockpits which fill with toxic exhaust gasses and cockpits which don't open above 350 kph) either aren't modeled in the game or aren't that much of a problem in your typical Quick Combat Dogfight.
And, yes, that's all realistic. The late war Soviet fighters came as a shock to the Nazis, and the Luftwaffe's recommendation was to not engage the La-5/La-7 below 3,000m.
As others have written, to win with a Bf-109G or K against a "Lavochkin" you need to use "energy tactics," meaning you need to be climbing, looping, and diving to get your kill rather than just making ever tighter flat turns. YouTube has thousands of videos from IL-2:1946, IL2:BoX, IL2:CloD, DCS, as well as other decent simulators (i.e., NOT World of Warplanes or War Thunder) which will show you how to use "boom and zoom" or "energy tactics" while flying a Bf-109G or K. Many of them even specifically show how to defeat the La-5 or La-7.
Additionally, you want to use the Bf-109's slightly higher top speed and slightly better climbing ability to "drag your opponents upstairs". That is, try to get them to go higher and higher until they're fighting at your preferred altitude rather than theirs. If they won't play that game, gain lots of altitude so you can "separate" (increase distance) or "merge" (close distance, ideally making an attack when your flight path intersects or matches your opponents') both vertically and horizontally.
If you're using energy tactics and you get significantly below your opponent at any time, you're doing something very wrong.
Additionally, your gunnery - especially your deflection shooting - needs to be much better when you're energy fighting, since typically you will be forced to make attacks at a high angle of deflection. This is because your opponent is typically more maneuverable than you are and will "turn into you" to spoil your aim as much as possible.
Edit:
While it's for IL2:BoX, this is probably the best of the "Use E Tactics to win in a Bf-109G vs. a La-5" videos. Clearly, the creator has a pretty good grasp on how to do WWII-style combat flying and he doesn't make too many mistakes while getting his kill:
The Bf-109G-6 and La-5 will handle similarly enough in IL2:1946-modded that the info is applicable.