I can answer one of those. The vehicle in the picture is a typical SdKfz 251 half-track, tons of them were produced. The rockets aren't an integral part of the vehicle itself, they are addons called Wurfrahmen, literally "launch frame," hung on to the side of the vehicle. You can see dozens of discarded frames lying on the side of the road in the picture, they were modular and very cheap to make and use. While the 251 half tracks were what most of these frames were attached to, many were also attached to captured French Renault tanks, I believe. The half-track could continue to be used as an APC after the rockets were installed, so it was a cheap and effective way to give mobile infantry a heavy artillery punch without having to lug around a towed rocket launcher or artillery piece with a separate, dedicated crew.

I can answer your question about german armour on the western front. Tigers and Tiger IIs were virtually impervious to allied armour on their front glacis except for a lucky shot to the turret ring even then it was slim. Later on in the war the British introduced the Sherman Firefly which mounted a 25 pounder cannon that was similar to the 76.2 cannon in the T34/85. The firefly could penetrate fron Tiger armour at close range. The only way for other medium tanks to defeat the Tiger was to swarm it and hit it in the flanks or rear where the armour was thinner. Any tank could immobilize it by hitting it in the tracks and then have infantry swarm the tank. More risky but you gotta do what you gotta do.

The difference between an assault gun and a tank is that assault guns don't have a formal turret super structure. You can change the azimuth of the cannon up and down for range but to traverse the gun the whole vehicle had to pivot so it was great on defence but not so much on an attack. The reason they built assault guns is they were cheaper and quicker to produce due to the complexity in german turret systems

The Sten was derived directly from the Lanchester which was itself derived from the German MP28. All of these being chambered for the 9mm Parabellum round. The MP38 and MP40 are for most purposes the same weapon, the MP40 being a refinement for manufactureability and the Sten mag was based directly on the MP38, differing only in its length and capacity, with the MP38/40s having 40rd mags with the Sten having 32. The Sten was not specifically designed to be interoperable with its German counterparts, but it worked out that way, they fit, but not always well, same dimensions, differences in manufacturing tolerances. And just a minor nit pick, there is a difference between a magazine and a clip, a clip is a simple spring device for holding a small number of rounds, typically 5, in the case of the M1 Garand rifle 8, generally discarded after use, magazines were designed to be reused indefinitely. The clip is used to rapidly load a fixed magazine such as in a Mauser, Enfield or such, or in the case of the Garand, remains in the weapon until expended. (please excuse my rambling on)

1. Yes. It proved to be the Sten's major weakness. The MP40 mags were double row, single feed. The mag lips had to centre the rounds. The lips were easily bent and misfeeds were the most common malfunction.
2. Dunno
3. The PIAT was used and did knock out some Tigers, similarly the 3.5" bazooka with the US troops. It was a close range job and the cahnces of sucess were small. The Brits fitted a 17 pounder AT gun to Shermans to make the Firefly, which could take out Tigers. Mostly I think they relied on airpower to reduce the Axis armour.
4. Dunno.