The BIble teaches that all three dwell within us, the Father, the Son, and the Holy Spirit. So praying to any one of the three does not put them outside ourselves, nor dioes praying bring them inside. Rather, asking them to dwell within us is what brings them into our lives, and into our souls. As the Holy Spirit dwells within us, he can hear us when we are distressed, but not sure what to pray for. We can tell him that we are not knowing what to pray for, and he can then read our hearts and know what we need, and then plead to the Father on our behalf.
The Trinity is not really discussed in this presentation ... but I guess could be implied. However, your suggestions does not violate the concept of the Trinity. Given again that the Father and the Son also dwell within us, then is praying to someone who dwells with you puts them outside yourself ... what does that mean? Nothing, really.
At this point it can only become paradoxical indeed. As prayer always is.
My point was, Trinity is basically a structure, a
gtheometry, where the distinction of "persons" in position and function must be posited before being denied, or corrected (as by the Cappadocian doctrine of perichoresis or "mutual indwelling").
This structure is more or less adequately reflected by the liturgy. Any liturgy from this perspective is theologically better (to me) than the spontaneistic soup of most "non-liturgical" churches. While the invocation to the Son or the Holy Spirit plays a specific (and limited) role in the liturgy, out of the liturgy it easily turns into a meaningless fad.
though in Greek grammar he is referred to both as "he" and as "it" which either are proper terms for him.
Pneuma is a neuter and can only be referred grammatically as such. But it can be verbally identified to masculine figures such as the Johannine paraklètos or feminine ones (in Gnosticism or Judeo-Christianity, there depending on the feminine gender of ruach).
the communion of saints is the church's most beautiful doctrine
I tend to agree with this "aesthetical" judgement. Perhaps because it comes close to the very essence of "religion" -- think of the ubiquitous "ancestors' 'worship'".