As I know, when an element is introduced for the first time, it is generally preceded by an indefinite article ('a' or 'an'). Although some exceptions exist for “means” and plural recitations. However, my question is if an element (uncountable noun such as 'water', 'air' or the like) is introduced for the first time, do I have to add an indefinite article preceeding it? It looks werid to have "a water", "an air" or the like. Is there any precedents or legal basis (e.g. something from MPEP or 35 U.S.C., etc.) can be used?
Do I have to add an indefinite article preceeding an uncountable noun?
No. This would be ungrammatical English.
It appears you might have the wrong end of the stick by suggesting that an element introduced for the first time is generally preceded by the indefinite article.
In fact, the problem arises in the other direction: when the first use is introduced by "the" or "said". This gives rise to a lack of antecedent basis.
That is, MPEP § 2173.05(e) provides:
A claim is indefinite when it contains words or phrases whose meaning is unclear. … The lack of clarity could arise where a claim refers to “said lever” or “the lever,” where the claim contains no earlier recitation or limitation of a lever and where it would be unclear as to what element the limitation was making reference.
Thus it would be entirely correct to refer to air or water without the indefinite article, since this does not imply that air or water has been previously discussed, and thus does not introduce a lack of antecedent basis.
For completeness, it would also be correct to rely on an inherent antecedent basis in some cases. The canonical example is "the major diameter" of a previously introduced ellipse, since all ellipses inherently have a major diameter.