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Biblical Unitarians have a wide range of views about a wide range of subjects - the term simply groups together people who believe God is the Father, not Jesus, and also hold that the Bible has authority in a strong sense (as opposed to other forms of Unitarianism which view the Bible as having authority in a weaker sense). Biblical Unitarians are a faction within Christianity, not a specific denomination.
Question 1. is highly relevant to the defining features of Biblical Unitarianism. If Jesus is not God, is it OK to pray to him?
The answer commonly seems to be yes, but there is debate.
The article Can We "Pray" to Jesus Christ? from BiblicalUnitarian.com addresses this question.
"There is a controversy among Christians who believe that Jesus is not God but the Son of God, about whether or not we can pray to Jesus. The only definitive place to go for an answer to that question is the Word of God. [...] We believe that the Bible makes it clear that one can pray to Jesus, but does not have to, and we will do our best to show why that is."
This is perhaps similar to the debate between Protestants and Catholics about whether praying 'to' Saints is OK. Different people have different views.
In particular, Jesus seems to say we can ask Him for things. John 14:14
"You may ask me for anything in my name, and I will do it."
However, there is debate about whether this means addressing the prayer to Jesus, or addressing the prayer to God in Jesus' name, which Jesus unambiguously says we can do.
So the answer to 1. is 'yes' for at least some Biblical Unitarians. Even there, though, the emphasis is perhaps different from standard Trinitarian practise.
"Those who enthusiastically embrace the idea of praying to the Lord Jesus must recognize that this practice ought not to be carried out to the point of distracting one from the worship of the Father. We are sure that the Lord Jesus would find it ironic indeed if he himself were to become the principal object of Christian worship and adoration, when his entire life and ministry was devoted to the glorification of his Father."
For question 2., as the OP points out, there are instances in scripture where people seem to 'hear' Jesus. Since that's the case, I don't see why Biblical Unitarians would object to this idea.
Question 3. moves away from something specific to Biblical Unitarianism, presumably a prayer could be answered unambiguously.
Question 4. is an empirical question, but really two questions. Has someone had an experience like this? Were they having a veridical experience? I'm sure a Biblical Unitarian has done this, but I don't have a link to reports of this.