The armament and engine was better in the La-5 than the Yak-3  I like the Berezins. The flight characteristics  above 3000 meters was inferior in the vertical and the roll.  Control systems layout and pilot ergonomics were AWFU:L. Loss rates because of the stupid cockpit layout was the highest among Soviet type target defense interceptor for pilots killed trying to move all the damned levers and switches. Head down in the Cockpit disease was the cause. The Yak was simpler to fly. 

The La-5 was a DEATHTRAP.  I don't know that much about the La-7 improvements to correct the La-5 faults, so I don't know if the pilot management load was ever corrected enough. The La-9 postwar certainly addressed those issues and was the fighter the Russians really wanted in 1942.    

H. 

Nope. Pretty Boy Willy's witless crew  FUed the design  so badly that even with the fighter go-ahead and without Hitler's meddling, the defective tail *never really fixed , the fouled  up gun pack (also never really fixed) and the screwed up landing gear would still see a service entry date of late 1944, and with ALL of those critical defects still present.  

Heinkel 280...

Heinkel was a better engineer and a better PILOT. That would have made a decent mid 1943 entry and proved effective from the first as a strike fighter and a bomber killer as well as a general interceptot  It could be considered a jet powered replacement for the FW-190. In a panic, it could have been rushed into service mid 1942.