''I hunger for sand! I yearn for a desert, pining for a draught...''
Is this sentence (the second, that is) from above grammatically right? I mean, can I use the two present tenses, simple and continuous, in a combination like this?
The formation is not two different present tenses, it is a present tense and a participle together. In the same way, one might write
It flamed, red with the heat of the embers
Although it happens to be the adjectival form of a verb, 'pining' here is just an adjective, like 'red', and not a new verb.
The 'red' modifies 'it', and you omit the 'is' from 'It is red.' because you are modifying in apposition, as if you said
It, red with the head of the embers, flamed.
But you have subsequently reversed the phrases, which is permitted, especially since it removes an unnecessary comma.
In most cases, the answer is no—not without modification.
When you see constructions like this, generally one of two things is intended:
I yearn for a desert, and I am pining for a draught. (pining used as a verb)
I, while pining for a draught, yearn for a desert. (pining used as an adjective)
In case #1, the original sentence is intended to be a compound predicate: "I ( (yearn for the desert) and (pining for a draught) )." Here we are missing not only the coordinating conjunction, but more importantly the am before pining. So the lack of parallelism works against you, and the form is ungrammatical.
In case #2, "pining for a draught" is an appositive used to provide amplifying information to the subject (I). The problem is that it's been placed too far away from the noun/pronoun that it's describing. Moving it directly after I (and setting it off with commas) makes it well-formed: "I, pining for a draught, yearn for a desert."
Without one or the other modification, however, the sentence is ungrammatical.