Can glass be made with anorthite?
In theory, yes it is possible. In practice, not really.

First of all, the anorthite on the moon is never pure anorthite ($\ce{CaAl2Si2O8}$) but rather an anorthite-albite ($\ce{NaAlSi3O8}$) solid solution. That is, the single crystal contains both components. The diagram you added there, where it says "mole %"? The other stuff is albite.

Now, back to glass making. Just about any crystallite solid silicate can be made into a glass. The process is simple: heat it up above the melting point, and then cool it down fast enough so it quenches to glass instead of crystallising. Let's look at these points in details.

Melting the stuff: Anorthite has a very high melting point: 1553 °C. Forsterite (the Mg-rich end member of the olivine group) has an even higher melting point: 1890 °C. To melt the stuff you're going to need a furnace that can go that high, and your energy bill is going to be extremely high. Here's a liquidus phase diagram of the $\ce{CaAl2Si2O8-Mg2SiO4-CaMgSiO6}$ system so you can get an idea of the temperatures required:



Luckily, your material is not pure anorthite. It also has albite! That's good because it takes the melting point down:



However, 1100 °C is still pretty high. The glasses that are commonly used in industry today have melting points of below 1000 °C. This is achieved by having high contents of sodium in the glass, which is perfect in taking the melting point of the material down. However, materials on the lunar surface are not that rich in sodium, and that's a problem.

Adding iron to forsterite (i.e. the fayalite component of the olivine group) will take the melting point of it down, but pure fayalite melts at around 1200 °C which is no good, and the iron will colour the glass green to dark brown (seen as black if thick enough), depending on how much oxygen is around. More about iron later.

Cooling the stuff down: Silicate glasses that we know and love contain abundant silica, commonly above 70%. This makes the glass very viscous because of Si-O polymerisation. A viscous glass can be easily left to cool in air (by the way - not readily available on the moon) and it will remain glass. Cooling a non-viscous glass that has below ~50% silica in air will cause crystals to form in it (anorthite in your case) and it will not be perfectly clear anymore. Therefore, you need to cool it very rapidly, by quenching in water. The problem now is that the glass is very brittle and will most likely crack during cooling or very soon after (this is from my own personal experience in trying to make glasses of these compositions).

So far we have two problems: melting it, and cooling it. There are other problems. You were worried about impurities and rightfully so. Iron is your biggest enemy. Even trace amounts of iron (&lt; 1%) can make your glass dark green or brown. Not only that, if there is oxygen around you might even have magnetite crystals in your glass and it's going to be completely opaque. You need a way to get rid of the iron. Nickel is also a minor problem. As for other "impurities", such as Al, Na, K, Ca, Mg, that's not a problem. They don't give any colour to the glass. It's the transition elements that you should fear.

Yet another problem is that you are not going to get pure minerals. The lunar surface does not contain blocks of anorthite or forsterite or anything else. The regolith is a powder made by weathering down of the minerals, and it contains a horrible mixture of everything. If you want to separate the anorthite or transition-metal-free stuff, you will need to figure out a way to do it.