Interesting question! I have never heard the Holy Spirit referred to as 'She'. I'm afraid I don't have enough knowledge to answer this question from a historical/linguistic point of view. But I'm not sure if the Holy Spirit is the same thing as Shekinah. In the New Testament it says:
(John 16, NIV)
5"Now I am going to him who sent me, yet none of you asks me, 'Where are you going?' 6Because I have said these things, you are filled with grief. 7But I tell you the truth: It is for your good that I am going away. Unless I go away,
the Counselor will not come to you; but if I go, I will send him to you. 8When he comes, he will convict the world of guilt[a] in regard to sin and righteousness and judgment: 9in regard to sin, because men do not believe in me; 10in regard to righteousness, because I am going to the Father, where you can see me no longer; 11and in regard to judgment, because the prince of this world now stands condemned. "
Someone correct me if I'm wrong, but it seems that when Jesus talks about the 'Counselor' He is talking about the Holy Spirit? I admit I don't know/understand that much about it. I believe in the Trinity, so the Holy Spirit is also God, and He is present on earth - in all who accept Him. So in a way, the Holy Spirit is a lot like 'Divine Presence' (Shekinah), but still different in other ways.
About feminine/masculine: I don't think that God is male/female (after all, both men and women are made in His image) - except Jesus. But I think the reason God is called 'He' is because His relation to us is 'masculine' (CS Lewis). That's just one explanation though.
It's interesting that you said "Shekinah is also associated with the Temple, and wherever 10 or more are gathered in prayer and with those in need, and with prophecy, special moments in religious history, special celebrations, etc., etc. "
In the Bible the Holy Spirit is sometimes mentioned in relation to prophesy, etc..and Jesus said that whenever a few are gathered in His name, there He is (but I don't know how the Holy Spirit ties into this).
Sorry I'm rambling now
I still have a lot to learn about the Holy Spirit - don't we all.
fea