There are two questions here and I will only answer the one about the article.
The function of the article ("the" in English and "ho" in Greek) are quite different and thus we have the following differences:
- Greek often has the article and good English does not
- Greek often does not have the article and English requires it.
Thus, have every variation of this in the names of deities:
- Greek often does not have the article before "The Father" but English requires it because "Father" is a title and not a name
- Greek often has the article before "Jesus" but English would not have it because "Jesus" is a name and not a title
- Greek often does not have the article before "Holy Spirit" but English requires it because "Holy Spirit" is a title and not a name.
In English, if we say, "Give this to the captain", "captain requires the article because it is a title and not a name. Greek does not have this requirement; hence the difference. The same is true of "the Son" which is a title and not a name so English needs it but Greek does not always have it.
Lastly, for a rigorous discussion about when the article is required and when not, see Greek Grammar Beyond the Basics by Wallace. Suffice to say here that the instances in Acts 2:4 about "Spirit" vs "the Spirit" is a perfect example of the first instance being in-articular and subsequent instances of a noun being articular because they are anaphoric - good Greek Grammar! This means that both are the same entity.
I will not comment on the interpretive practice of capitalizing the names of Father Son and Holy Spirit.