Reply from the historian.
License production of Junkers Ju 87D-5 was in full swing in Slovakia since 1943. The type was produced by Slovakian Aircraft Company (" Slovenská továreň na lietadlá") based at Trečianske Biskupice. Deliveries for the Luftwaffe and Romanian Air Force were a priority, so Slovakian Air Force with great delay only received 10 aircraft out of 50 examples ordered.
First four aircraft delivered in June 1944 were marked with civilian codes OK-XAA, OK-XAB, OK-XAC and OK-XAD. (There was no aircraft marked OK-XAE.) Further six Ju 87D-5 aircraft were delivered next month. Pilots of Letka 11 (11th Squadron) started training on the type. This was short lived however and the aircraft spent most of time stored at Spišska Nova Ves. At the outbreak of Slovak National Uprising in late August 1944 these aircraft were captured by the Germans. Junkers Ju 87D-5 was never flown in combat by Slovakian pilots.
Some of the Slovakian pilots I could link with flying Ju 87D-5 in summer 1944 were: J.Gerthofer, Kollár, Gajdoš, Sitár, J.Matiáš and S.Valent. Ján Gerthofer was third most successful Slovakian Bf 109 ace. He shot down 26 Soviet aircraft while serving with Letka 13 (13. Slow/JG 52) on the Eastern front.
I have no info if that was the case (re Czech Air Force operating Stukas). It is well known that many German aircraft were left behind on Czech territory after the capitulation. (Some, like Bf 109 and Me 262, were continued in production.) It is possible that some Stukas were found on the ground as well, but I don't know if any were flown by Czechoslovak pilots post war. I haven't really researched this topic, but in my opinion it is unlikely.