Yes they were.
Custom made marvels made by brilliant engineer craftsmen.
No, they were not. They were built to a plan with standardized parts for their model, there was no hand fitting of parts on production tanks, they were built more slowly due to much more stringent manufacturing tolerances and the fact that the Germans overwhelmingly did not use an assembly line process but the parts (and by extension the tanks) were all built to specific specifications and pieces that didn't meet those specifications were rejected and recycled. Just like any other industrialized nation at the time.
Could any random dude fix them? No.
Anybody who was trained to repair tanks could, as well as most people who were mechanically minded and had the parts on hand. This is the same as anyone else's tanks though. You can't replace pieces on a vehicle that size without having the piece on hand and the tools to do it. Were German tanks more difficult to repair? Sometimes yes and sometimes no, depends on how it broke and whether the parts were available should a replacement part be needed. Early in the war this was often the case and German armor worked very well, later in the war this was not the case and many German tanks were abandoned due to lack of spare parts.
Were there alot of them? Not really, Germany used old tanks for most of wars - Battle of France was mostly Panzer IIs.
The Panzer III had only been adopted the year prior in 1939 and so there just plain weren't very many of them at that point, had the Germans had more Panzer IIIs then they very likely would have used more. Now German manufacturing practices didn't necessarily help that but it wasn't uncommon for new vehicles from any nation to take a bit to show up in large numbers. The French were also mostly using old tanks, tanks which were contemporary to the Pz. II as a matter of fact.
The USSR had better tanks and far more of them.
Define "better". That's a super nebulous term and I need to know, specifically, what your criteria is before I can agree or disagree with you on it. Far more of them? Sure, that I will agree with you on. However one thing to keep in mind is that even if Germany
was some how capable of cranking out tanks on the scale of the USSR or the USA they would never be able to support them, they lacked the manpower reserves and natural resources of either of those nations and they would never have had the logistics corps capable of producing, let alone transporting, all the ammo, fuel, spare parts, etc. that an armored force that size would require. Germany was still using horse drawn carts as a serious part of their logistics train from the beginning of the war right up until the end. Another thing to keep in mind is that the Soviets did have massive production numbers but they also had colossal and consoistent problems with QC throughout the war due to the fact that they focused on total production numbers before anything else and so all throughout the war many factories cut corners on manufacturing.
What they lacked was trained crews and logistics system who could actually fix their vehicles.
Sure, maybe at first but once you get to late '42/early '43 they've (mostly) got they're shit sorted.
