Okay, no. Only the United States managed to design a usable proximity fuse during WWII, and that is an incredibly simple form of radar fuse, little more than a crude Doppler rangefinder.
What you're describing is full-up semi-active radar homing, the technology used in Falcon and Sparrow air-to-air missiles, and no one had a functional version of that until fully a decade after WWII. Moreover, those SARH guidance systems were for missiles, not cannon shells; the firing of a cannon shell is an extremely violent shock and it is *extremely* difficult to design electronics capable of surviving that shock in functional condition. This was actually the most difficult challenge in the development of proximity fuse technology, and is *specifically* where both British and German efforts failed. Moreover, SARH guidance is not standalone; it requires an actual guidance platform carrying a compatible radar system, which is another thing that does not exist for decades later.
To answer your questions straight up:
1. Yes, you can make even bigger siege cannons. The amount of resources required to create, support, and operate them becomes exponentially greater and greater. In addition, if they are designed for extreme range, they trade off payload. The "Paris Gun" was an absolutely enormous monster of a siege gun whose barrel was seventy meters long and which could fire to 130 kilometers range using only WWI technology; yet it was "only" a 238mm bore and the shell just a little over one hundred kilograms. In practical terms, such extreme-range guns were little more than propaganda gimmicks.
2. No, they can't be used to support ground armies. That is why the very large guns were classified as siege artillery, a category separate from ordinary heavy artillery. The lack of mobility and massive amounts of infrastructure required to operate them makes it impossible to use them tactically.
3. An anti-aircraft mounting for a siege cannon would be even more utterly enormous than the mountings for them already were, in order to support the massively heavy and long barrel at high elevations. They would be completely ineffective in the anti-aircraft role, due to their sheer size making it impossible to traverse and elevate them quickly enough to actually track an aircraft, as well as their rate of fire being far too low. An anti-aircraft gun of "normal" siege caliber would literally be lucky to get off two shots during the course of an entire battle; an even larger one such as you suggest would take so long to load even one shot that it would be impossible to use against air attack.
4. Firing at ships would require accuracy that is not possible without modern-style guided ammunition, which is impossible to make with WWII technology.