Parking is rather haphazard throughout Chile and is only really formalised in the big cities. Even there, cars wil park on the pavement or in ridiculous places. Play safe and find clearly marked parking areas or a public parking lot.
Some of the big cities have parking meters or ticket machines near the commercial districts but parking is still reasonably cheap. There are a number of big parking lots, covered and uncovered which charge more but are usually more secure. Elsewhere it seems you can park where you like but try to do it sensibly otherwise you'll generate an argument and potentially escalate it to the police being involved!
Enforcement of parking is done by the police and may involve a fine or your It's usually the police who deal with parking infringements and usually with a ticket and fine. Occasionally your car will be towed but it's not that common.
EU blue badges mean nothing in Chile but there are dispensations for disabled drivers. It's worth taking your badge with you as it may help to ease your passage to a more accessible spot.