Prodigious would definitely not be understood in the way you would be meaning it if you apply it to a person directly, like
Bob is truly prodigious. (not recommended)
However, you could certainly use it to describe their intelligence, like so:
Bob has a prodigious intellect.
If you simply want to say that someone is remarkably intelligent, I might recommend sticking with genius:
: a very smart or talented person : a person who has a level of talent or intelligence that is very rare or remarkable
: a person who is very good at doing something
: great natural ability : remarkable talent or intelligence
(from m-w.com)
While this is not an adjective, you could certainly use it descriptively, as in "He is a true genius".
The [finite form of to be] + present participle is used not only to denote continuous states or progressive actions but also informally, I submit, the ingressive or inceptive aspect, i.e., that an action or state has begun. Neither statal nor copulative/pseudo-copulative verbs are always exempted, especially in informal speech. There are other uses which have nothing to do with aspect but are used as intensifiers and polite hedges.
Some forty minutes into an hour baking time for fresh bread, the Malliard reaction is doing its magic:
That bread is smelling good.
I am not suggesting that the bread is in a continuous state of smelling good, but that the bread has begun to smell good (ingressive aspect) and it's time to get the butter out of the fridge, because I'm fixing to have a big slice of homemade bread (prospective aspect, but only for some speakers of Southern American English).
In a more formal register, I would say:
The bread is beginning to smell good and I'm about to have a slice of homemade bread.
Think of any food that looks unappetizing before cooking — steaks on the grill, a stew simmering for hours, dried beans — and wait for The Moment.
By like token, I could be mixing the hot and cold water to get just the right temperature for a bath or shower:
The water is feeling nice and warm now.
The water has begun to feel nice and warm now.
This apparently meme-worthy citation describes an emergent feeling of loneliness or contingency upon contemplating the vastness of the universe (ingressive aspect) using the meaning of seem as "seem to feel" and in the continuous form, accentuating a moment of intense emotion right now. It invites the reader to identify with the author in a way which to her apparently wouldn't be as rhetorically powerful as simply saying the universe seems huge. The universe, of course, has been huge since the Big Bang and it always is, but in this moment, she has begun to feel it.
At work he's a total jerk.
He is being a total jerk [today at work].
This usage is best solved by acknowledging a lexical difference: in the present tense one is making a judgment about his personality; in the continuous, instances of behavior, in this case, today.
Permanet states or non-animates without agency can never be used with the continuous:
*She is being Australian. (nationality, not in some odd scenario behavior)
*He is being short.
*My shirt is being green.
You are looking pale today.
You are looking fabulous today.
While the first sentence could be parsed as ingressive, this usage seems more like a polite hedge, while the second is best viewed as an intensifier which, like the meme, suggests a heightened level of personal involvement.
Best Answer
You seem to have two problems with the given sentence, so I'll try to address them separately:
Can prodigious be used to describe someone's language skills? Well, look at this definition of the word, along with a usage example (from Merriam-Webster.com):
Going by this definition, as well as the one you brought yourself, there's no actual requirement for something to be earth-shatteringly amazing to be considered "prodigious". It only has to be exceptional or impressive in context. There's nothing amazing about a supply of canned food, it's just a large amount. That seems to match the student's usage, since the reward specified (finding a job at a foreign company) seems to be unusual or impressive to match the skill.
You say the sentence structure is "neutral", but I don't understand what you mean. The only thing that can be considered "neutral" is the use of "decent", which might seem to understate the value of the job. You can replace it with a more positive adjective ("he can get a good/high-paying/lucrative/excellent job") without changing the structure.
If anything, his sentence structure sounds more natural and less stilted to me.