That '54 30" stove is very similar to my '56 GE Speedster 40" stove. If you PM me and give me your email address I can send you a schematic for my stove which I'm quite sure will be very similar. The two stoves will be wired in essentially the same way with some minor differences maybe.
If the broiler element is getting juice when it is switched to the Bake setting, there is a wiring issue likely at either the switch or fuse box. If the oven element is only getting slightly warm, you are only getting 120 V to the element and not 240V because the other 120V leg is not getting to the element. Likely you have a fuse blown cutting off power from one of the legs. Do not trust a visual assessment of the fuse to determine if it is blown or not. I had one go on my '56 last year and you could not tell it was bad by looking at it. I had to test it with a multimeter to determine it was bad. Also do not trust that the fuse marked as servicing the oven is actually doing that. Read on to find out why.
As for the bake element/broil element wiring problem, it may have occurred when someone worked on it and put the wiring back wrong but don't be surprised if things were incorrectly wired in the factory. I had some issues with the oven in my '56 last year and during the course of troubleshooting the issues, I found that the bake element was wired to the wrong fuse and whatever was supposed to be on the fuse the bake element was wired to was incorrectly wired to the fuse the bake element was supposed to be wired to. Knowing the history of that oven like I do (it's been in the family over 50 years), I'm 99.99% sure all that incorrect wiring had to have occurred in the factory. It didn't stop the oven from working, it just made it harder to troubleshoot a blown fuse because the fuse that was supposed to be in the bake element circuit wasn't actually in that circuit. If you don't know what fuse is actually in the bake element circuit then it makes it hard to find the blown fuse unless you check every one of the fuses in the fuse box.
You will not be able to tell if the oven thermostat is bad or good until you get both 120V legs to the bake element working so the oven can get hot. If, after doing that, the oven gets super hot and doesn't ever shut off power to the elements in order to keep the temperature from going way past the setpoint, then the thermostat is bad but you won't be able to tell that until you can get the oven hot.
As for the stove burners not getting as hot as they should on the high setting, it's probably that the burners have gone bad. Those old Calrod burners are different than most in that they are basically two burners nested inside each other. Different heat settings turn on different parts of the burner. When set on the high setting, all sections of the burner are given full power and so the whole burner goes red hot. One of the nested burners has probably gone dead so is not heating up when set on the high setting.
I had something like that happen with one of the 6" burners on my '56. The burner worked correctly on some settings but didn't all or did work but didn't get as hot as it was supposed to on at least one of the settings. I replaced the burner with a good one and the problem went away.
Before assuming you've got a bad burner(s), however, make sure that each of the burner terminals is properly connected to power and is getting the correct amount of voltage. There are 4 terminals on those Calrod burners instead of the normal two. If one of the terminals on the burner is not getting power then the burner will only work properly on some settings and won't work properly or at all on other settings. If you determine that you've got 120V at each terminal, then the burner is the culprit. Those burners are quite old so it wouldn't be surprising to find that they've failed in some way and just need to be replaced. I think you can still get them from GE although they don't say Calrod on them like the original ones did anymore. If not, try eBay.
PM me and I'll shoot you a schematic that should help you a lot.
I've attached a pic of my '56 Speedster. Notice how similar it looks to yours, just wider?
