How many transistors up top (NPNs)? Component Models? (SMD ONLY!) Does this design event make sense?
No it doesn't make any sense to have 1kW dissipation and ask for SMDs.
In the typical linear benchtop power supply (I have 30V 5A ones) there is a transformer with multiple output voltage taps, with a bunch of relays to switch them, so the pass transistor only has to drop a few volts, which reduces its dissipation and makes it more friendly to SOA.
Basically if you want a fully linear variable 30A power supply get a bunch of cheap benchtop linear supplies like Korad KD3005P and wire them in parallel. It will be cheaper and with better protection. Note the schematic in the question has no protection. In case of output short it will just shoot all the power transistors into orbit.
First, why is the output not regulated while input changes? (Input is AC 10 V with a DC offset of 20 V.)
Because Q2 runs out of hFe at high current. A real transistor would also run out of SOA and burn.
Second, why the R1? a why such a low value, almost 650 mA goes through it! that will fry it and also waste a lot of power.
That's normal, you don't want a high value resistor because that would increase open loop gain too much and make it unstable. Even with this low value, stability of this circuit is very dubious.
Last any tips?
Yeah, for this current and voltage, it's the same as a motherboard CPU VRM, so same solution, use a synchronous multiphase buck DC-DC.
The whole thing will be cheaper than just the heat sink for the linear regulator.
Because basically, if you use a linear regulator, it's because you need very low noise for a sensitive low current circuit, and don't want to bother with filtering out the noise from the buck. Or it's a bench power supply: I bought a pair of linear ones because when I see some funny noise stuff on the scope or in measurements, I don't want to have to investigate to find out if it comes from the switching supply or not.
But what kind of load draws 30 amps and requires very low noise?