Yes. Because both oxygen and carbon monoxide bind to the same site on hemoglobin, they compete for binding to hemoglobin and CO is therefore known as a competitive inhibitor. Since carbon monoxide binds hemoglobin very strongly, small concentrations of carbon monoxide can out-compete moderate concentrations of oxygen for hemoglobin binding. However, one feature of competitive inhibition is that very high concentrations of the substrate can out compete binding by the inhibitor. The way to think of this is that when carbon monoxide falls off of hemoglobin, there is so much oxygen present compared to carbon monoxide, that it is much more probable for oxygen to bind despite oxygen's lower affinity (it's not necessarily the case that the oxygen actively causes CO to break appart from the Hb, just that it prevents the reassociation by binding Hb before CO can). (For completeness, I'll also note that there are other types of inhibitors called allosteric inhibitors. These types bind to separate sites on hemoglobin and sometimes cannot be competed off by providing large amounts of substrate).
Now for your second question, the increased oxygen concentrations will be in the lungs, so the carbon monoxide falls off in the lungs where it can be exhaled.