'Breaking in', sometimes also called 'running in', is the period when components in the engine, like the rings and bearings, work in the surfaces they are in contact with. That's the rings with the cylinder bores, the bearings with the crankshaft, the cam bearings with the camshaft etc. It's best in that time that you don't drive it hard under load or at high speed, and it's a good idea to vary the engine speed so you're not driving it at the same speed all the time. Engines in today's new cars don't need much running in at all, according to the carmakers, but older engines do and it's a good idea to give them 1000 to 1500 km to settle in. Swap oils at the end of that period and you could use a 20W-50 oil at that time.

TO RUN it at its best on unleaded you should fit hardened valve-seat inserts to the head, lower the compression ratio and retard the spark a little to suit the lower octane rating of unleaded. You're talking about $1000, so I'd think long and hard about doing that on an old car like your XE. I'd run it on unleaded and add an upper-cylinder lubricant.

I would run it on petrol one tank in four. Regularly running petrol through the system keeps the rubbers and seals in your fuel system moist and able to do their job, letting them dry out can lead to leakage and other problems. To your other question. Yes, petrol can spoil when left to sit in the tank for a long time. Moisture can accumulate, it can become gummy and then clog up the system when you use it.