I am a chemist, so maybe I can say a few words that might help.
First of all, let's tackle the easy part. Sodium hydroxide is a strong base, which means that when it dissolves in water all of the anions (i.e. negative ions) in sodium hydroxide become free OH-. Note the "-" sign in OH-. It's important because it means that OH- is negatively charged. Basically, OH- is, by definition, a base. (How do you like the play on words in the last sentence?) This more or less repeats what some of the other comments have said.
It becomes more interesting when it comes to the carbonate system. There are three parts to the carbonate system. The first is carbonic acid, H2CO3. It is a weak acid, which means that when it dissolves in water some of the molecules break ("dissociate" is the technical term) into H+ and HCO3-. The rest of the H2CO3 molecules stay intact. (Actually, it more like a dance, where at any instant some of the H2CO3 is breaking apart into H+ and HCO3- and some of the H+ and HCO3- is getting back together to form H2CO3. This is called "dynamic equilibrium".)
The next in the carbonate system is bicarbonate, HCO3-. When sodium bicarbonate (NaHCO3) dissolves it releases free bicarbonate into the water. Bicarbonate is "amphoteric", which means that it can act as either an acid or a base. It can react with water to form OH- plus H2CO3, or it can dissociate to form H+ plus CO3--. As it turns out, the reaction to form OH- plus CO3-- tends to predominate, so on balance bicarbonate is considered a weak base.
The third item in the carbonate system is carbonate itself, CO3--. It is a base because it can react with water to form OH- and HCO3-. However, when sodium carbonate dissolves, not all of it reacts to form OH-, so although CO3-- is a base, sodium carbonate is not nearly as strong of a base as sodium hydroxide. It is, however, a stronger base than sodium bicarbonate.
You can make solutions that are intermediate between the items in the carbonate system. For example, you could make a system containing H2CO3 and NaHCO3 by dissolving some baking soda into selzer water. The solution would then contain some H2CO3 and some free bicarbonate ions, HCO3-. This solution will act as a buffer, which means that it tends to resist changes in pH upon the addition of either H+ or OH-. This buffer system helps keep you alive because it is an important one in your blood. If your blood becomes too acidic or too basic then you die. The H2CO3/HCO3- buffer system in your blood helps prevent that from happening.
You can make another buffer by making a solution from sodium carbonate and sodium bicarbonate. The solution will contain both CO3-- and HCO3-. This CO3--/HCO3- buffer is more basic (i.e. has a higher pH) than the first buffer system I mentioned. It is also much less basic (i.e. has a lower pH) than sodium hydroxide.
What happens when you start adding sodium carbonate to a sodium hydroxide solution? As far as pH is concerned, not much will happen.
However, if you add sodium bicarbonate to a solution of sodium hydroxide it gets more interesting. At first the bicarbonate will react with the hydroxide (HO- is hydroxide) to make CO3-- while reducing the amount of OH- in solution. This lowers the pH, i.e. makes the solution more basic.
If you add more bicarbonate to the sodium hydroxide solution you will eventually get to the point where you have neutralized all of the OH-, and you now have a solution of pure sodium carbonate.
If you add even more bicarbonate you will have a solution containing both HCO3- and CO3--. That solution will be a buffer. At first it will have more CO3-- than HCO3-, the pH will be high, and the buffering capacity will be weak, i.e. the ability to resist changes in pH will be weak. If you add enough bicarbonate so that there are equal amounts of CO3-- and HCO3- then the buffering capacity is at it's maximum. Also, the pH of the solution will be at the same value as something called pKa for bicarbonate, which is 10.3. (I am simplifying the discussion because there are other effects, such as "ionic strength" that can shift the values somewhat from their theoretical values through changing something called "activity coefficients".)
If you add more bicarbonate then you will have a solution with more HCO3- than CO3--, and the pH will be lower, and the buffering capacity will be weak. It will, however, still be on the basic side of the pH scale.
Another way to more or less the same end is to add carbonic acid to a solution of sodium hydroxide. You can convert it to a solution that is a mixture of sodium hydroxide and sodium carbonate, and adding even more will make a solution of pure sodium carbonate. Adding even more than that will get to you a mixture of sodium bicarbonate and carbonic acid ( a buffer). Add more carbonic acid and you get a solution of pure sodium bicarbonate. Keep adding carbonic acid and you get a mixture of bicarbonate and carbonic acid (a buffer at a lower pH).
If you add CO2 to water it makes carbonic acid. (There are some subtleties about that I won't discuss here.) Natural air has a little bit of CO2 in it. One consequence of this is that if you leave a solution of sodium hydroxide exposed to air it will eventually be converted to sodium carbonate, with a corresponding drop in pH. (In principle, it could even react further to make sodium bicarbonate.) Therefore, if you make sodium hydroxide solutions you need to keep them capped. Otherwise, you will lose sodium hydroxide by conversion to sodium carbonate and the pH of the solution will drop.
Anyway, shifting gears a bit, if you add an acid to a solution of sodium hydroxide and para aminophenol, you will eventually drop the pH of the solution enough so that the para aminophenol (which is a negative ion in highly basic solution) becomes a neutral molecule. The neutral molecule is less soluble than the ionic form, and you may get precipitation of the para aminophenol. Adding more acid will eventually convert para aminophenol to positive ions, and then it will dissolve again.
