On Type 1 v Type 3, the latter was more like most Western fighters not only in armament and protection but range: relatively short. The Type 1's range was important in the early-mid 1942 campaigns, as was the range of the even longer legged Navy Zero, and the Type 1 had good success v most Allied fighters in that period, there was no crying need for something better. Even when introduced in New Guinea in 1943, the Type 3 was not obviously superior as far as the Japanese were concerned. Some Japanese pilots still felt an alert pilot in a more manueverable plane (like the Type 1) could foil 'hit and run' attacks by turning into them. Also the early Type 3's had serious servicibility issues in New Guinea. The Type 3 was clearly superior in intercepting bombers.
On Type 4 as usual it tends to come down to 'sim game' mentality v historical perspective. Sim game mentality seeks out a single 'truth' about a/c aerodynamic performance to program into the game, a game without certain reproduceable performance for the a/c would be frustrating to play. A historical perspectve realizes there are simply uncertainties in some cases. It's just not certain what the actual speed capability of real Type 4's in real operating units actually was, and probably wasn't uniform anyway. In actual combat, Type 4's had a relatively unimpressive record, including probably worse than 1:1 v late model P-40's in China, though it did better against advanced Allied types than the Type 1 did in the same later period. The Type 4 also had servicibility issues in early use in 1944, which counters the idea of 'well made' early Type 4's v 'poorly made' later ones. You had the technical maturity curve of the new design or a/c and engine particularly, going in the other direction.
The Type 4 was more advanced and capable than the Type 1, which had remained the most numerous Army type up to 1945, but as far as being more effective than its opponents, history is a question of what was, not what could have been. Which of the Japanese Army fighters enjoyed the greatest operational success? the Type 1, in 1942 and some cases (v the British in Burma for example) well into 1943.
The Type 5 had no official name. There is no example I know of of Type 5's having any great success v US fighters, and even as of July 1945 the a/c is described in a Japanese account as 'just having the bugs worked out'.
Joe