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A Biblical Unitarian appendix to Biblical commentary Appendix 6: Usages of "Spirit" lists 15 different senses for the term 'spirit' ('pneuma' in the Greek) in the Bible.
However, as Appendix 11: What is the Holy Spirit? says:
"“HOLY SPIRIT” is primarily used in two very different ways: One way is to refer to God Himself, and the other way is referring to God’s nature that He gives to people.
So the first sense is a synonym for God. The second sense itself has synonyms. For example, the 'Helper' mentioned above in John 14:16 is another name for this second sense, so 'holy spirit' as a gift.
"18) The gift of holy spirit as “the helper” [...] The “holy spirit” is identified as a “helper” to believers in John 14:26. [...] The helper (the holy spirit) is sent by the Father (John 14:16-17) and Jesus (John 16:7). It does not speak on its own, but it speaks only what it hears (John 16:13). Thus, the gift of holy spirit is directed by God and Jesus, which is what we would expect since it is God’s nature born in us."
So Biblical Unitarians would understand various uses related to the holy spirit as mapping onto either of the two senses described above, and the second sense of a gift can be directed by either God or Jesus. As examples of both instances of the second sense from your list above, 'Helper', 'Spirit of truth', 'Spirit of your Father', 'Holy Spirit' = gift from God. 'Spirit of his Son' = gift from Jesus.
However, as mentioned, sometimes uses of 'spirit' would map onto other senses as listed in Appendix 6 above.