Each observatory increases the chance to auto-observe, but the chance will never be 100% because it diminishes after 75%.

The relevant part of the code is the following (inside calender.js):

var autoChance = this.game.bld.getEffect("starAutoSuccessChance");  //in %
            var rand = this.game.rand(100);

            if(
                (this.game.ironWill && (self.game.rand(100) <= 25)) ||
                (rand <= autoChance)
            ){  
                dojo.hitch(this, this.observeHandler)({}, true);
            }

Every observatory increases your starAutoSuccesChance with 1, so 11 in your case. However, this.game.bld.getEffect does the hyperbolic effect which makes sure the chance does not become 100%. In another answer(which deserves more upvotes imo) this is perfectly explained, so I will not do it again.

Here you also see is that the chance is compared with a random number under 100 (rand <= autoChance) so the autoChance (or starAutoSuccessChance untill 75 observatories) is indeed the percentage of auto-observes.

When you run out of a required resource, mints and smelters simply do nothing that tick. That results in you getting benefits proportional to the resources you do have available (although the sidebar numbers won't reflect this).

Most buildings that consume resources have the same behavior, but there are some exceptions:

• If you run out of uranium, all of your reactors will turn off
• If you run out of oil, one magneto will turn off per tick (1/5 of a second) until your oil supply is positive again