My main reason for suggesting an electrician, is because I don't think there is a need for a tertiary cutout, but if the OP thinks it is needed then there is probably a need for a relay. That is what the OP asked and I was giving a reply that I hoped included due diligence. A sparks would be...
You would need to ask an electrician about the following: It may be possible to wire the immersion in series with a cylinder thermostat (possibly using a relay). As I said, ask an electrician.
In that case make sure that the joints are good and can't suck air. Might be a good idea to have the level of oil above the oil pump and be sure to purge it all of air before running it. It should then be capable of running the tank dry, which you don't want to do. That last foot of oil will...
You have a plastic tank, so don't put too much stress on it when rising. Make sure its new base supports ALL flat areas of the bottom and extends a few inches beyond the base area of the tank. I cant see an isolation valve between the tank and filter. Perhaps it forms part of your gauge or is...
You can get deaerators with a vent that can be piped. I would suggest that with the bottom of the tank only 300mm below burner, that an ordinary single pipe could be used without deaerator or lift pump. Maybe even rise the tank a foot, but should work as is.
I used welded mesh covered with 1.4" netting wire. I covered the top with a piece of plastic bottle to stop them reaching in and pulling food towards them. Food needs to be in the centre and out of arms reach. I also covered the supporting stake with split large bottles to make the stake too...