I'm not familiar with regulations and expectations in Clinton Hill, but in general for Brooklyn:
Is this legal?
Yes, and it turns out, necessary.
Is it safe?
Different neighborhoods have different levels of safety, and I'm not sure how to compare to where you live in Ecuador, but most people who own a vehicle in a residential neighborhood do it.
Is it possible (or advisable) to leave your car overnight parked on the street?
There is very little parking in the residential neighborhoods, so almost all of the residents leave their cars parked in the streets over night, as there is no alternative.
On thing you should be aware of is alternate side of the street parking rules. These rules are in place to allow for street cleaning and the specifics will be posted on signs in your neighborhood. The general rule is that on a specific day of the week for a specific time window, no parking is allowed on one side of the street. You may not get caught, but if the street sweeper shows up and your car is parked on that side, you will get a ticket and possibly towed.
As an example, for your street maybe Tuesdays from 8-12 you can not park on the left side and Wednesday from 12-4 you can not park on the right. This has become a way of life in these neighborhoods and if you are around at the start or end times you will often see people watching for an open spot so the can move as soon as the time changes.