Yes, 1N4001 would work but I’d usually go for 1N4004 or higher since it’s almost the same price for a higher voltage rating.

They are just generic TO-220 aluminium heat sinks. Here is an example: https://www.taydaelectronics.com/heatsink-to-220-4-fins-aluminium.html

Thanks Simon. I realised in retrospect that I should probably be able to power everything from +12 / -12 – I will do some tests with that and hopefully that will simplify my build. Otherwise I will look into your suggestion. At first glance the original board seems to take a similar approach.

For low current applications, you could probably chain LM7809 +9V and LM7909 -9V regulators onto the +12V and -12V outputs (similar to this circuit). The components in my circuit above would stay the same, but you would add another 100uF capacitor on the 9v outputs. You should have a look at which components are used on your old circuit board; they probably are very similar to this. If you require larger currents most modern circuits now tend to use switching mode power supplies since they are more efficient than linear voltage regulators; however they are trickier to build as a hobbyist!