When you compress the fuel air mixture (the 'charge') it gets hot. The hotter it gets the more chance it has to detonate (or 'pre-ignite'). The 'octane' rating of a fuel is a measure of its ability to resist detonation due to heat.

Increasing the compression ratio on a motor results in more torque throughout the entire rev range. Its simple thermodynamic law and is the very basis why engines compress the mixture to begin with. If you increase the compression by 10%, expect roughly a 10% torque increase providing detonation and ignition timing is not affected. Bear in mind that if it was as easy as that, then all stock motors would have compression ratios of 50 to1. There is ALWAYS a compromise (ie downside).

Increasing compression increases how much heat is transfered to the block, head, pistons, ring, valves, oil, etc in the engine. You will need to consider the radiators ability to dissipate this heat. Road cars have periods of low speed. Traffic lights and McDonalds drive thru will cook a high compression motor with a stock radiator. High octance fuel is more expensive. It's harder on the starter motor and battery and cold weather starting will deteriorate. The engine will also idle rougher (not as smooth).

So running high octane fuel in a stock motor is a waste of money. But running low octane fuel in a high compression motor will lead to detonation and damage to your engine. The obvious question is how much octane do you need for a given compression ratio.

It depends very heavily on the cam you using, correct spark plug use (may not be ok to use factory type plugs) and the pistons and rings you use. Generally speaking, if you want to remain on premium unleaded fuel and have high quality pistons with chrome top rings, an upgraded radiator and don't much road driving you should limit your compression to about 7.5:1 DYNAMIC. For a road car, use something more sensible like 7:1

From here you can then use your cam figures to determine the maximum STATIC compression ratio you can run without running into detonation problems.

The kidney shaped combustion chambers are designed to provide 'squish'. If you had a large flat sheet of MDF (about 1m x 1m x 16mm) rested one edge on flat concrete then allowed the MDF to fall onto the ground you would notice there isn't much sound at all. During the last few mm of the fall, the air between the MDF sheet and the concrete act as a cushion. The air escapes this gap at very high speed. If the floor was dusty a big cloud of dust would emerge. That's squish.

In a combustion chamber, squish does one very important thing. By keeping the mixture turbulent it means that hot spots in the head do not get the chance to super-heat a part of the mixture and ignite it. So basically it allows the use of a higher compression ratio.

Race engine builders pay very close attention to squish. It's difficult to work with as connecting rod stretch and expansion due to heat affect this dimension. When race engines over-rev and destroy and engine, its often due to the piston slamming into the head because of rod stretch.

Hope this helps.