He further explained how the water enters into these pockets via various fissures both from our oceans and other bodies of water (noting some study from last year where researchers found incredible volumes of water 700 kilometers underground).
First of all, the chemical and physical behaviour of water is completely different when you compare ocean floor settings and the deep mantle. Water may flow in fissures under the ocean, but once you get to several 10s of kilometres deep, the rocks become ductile and water can no longer flow in cracks and fissures. Regarding last year discovery of water in the mantle - this is really a sad story of poor science communication. What was actually discovered was that a certain mineral can contain water in its crystal structure. It's still a solid mineral and still a rock. Same like the water in concrete - it's not actually liquid water. See these two questions for more info:
Do ringwoodite minerals point to an "ocean's worth" of water, or a true subterranean ocean?
One side note was regarding the contents of magmatic rocks being surprisingly high in alkali metals, etc.
Most magmatic rocks contain a perfectly reasonable amounts of alkali metals. There are some rocks that have high alkali contents (and they have funny names too!), but this is not something that requires a different explanation from what is known so far from experiments and other studies. Yes, there are rocks with abnormally high alkali contents, and there is still research going on in that subject.
but I was out of my depth
I think this is the key word in here actually. Perhaps that professor was "dumbing down" his ideas to make it more accessible? This occasionally happens with us scientists, and in a lot of cases the listener simply understands something completely different from what the scientist meant. Another example of poor science communication, unfortunately.