How & why did the spirit of Jesus stop Paul from entering Bithynia to preach?
There are really two aspects to this question but only one aspect has been covered 'so far' in the answers already given. Various sound reasonings for being initially forbidden to preach in Asia, and then to not subsequently be permitted to enter Bithynia, have been expressed and I will not therefore reiterate those speculations here.
The second aspect concerns the OP's point 3. The apparent difference between the Holy Spirit and the spirit of Jesus.
In Acts 16:6, we find the words the Holy Spirit being responsible for an act of forbidden approach ... For the non-trinitarians amongst us (of which I am one), I see this as the collective spirit/active force of God & Jesus, having already/previously been infused into the minds of Paul & Timothy, informing them that there was to be no preaching in Asia ... God Himself therefore (along with Jesus), making it known, in no uncertain terms, that there is to be 'no' preaching in Asia, at least for the time being. Whereas , and here's the difference, in Acts 16:7, the spirit/active force, of Jesus only, suddenly is imparted to both Paul & Timothy, with regard to the lessor directive, that entry into Bithynia is also not to be permitted.
On the question of whether the translation in Acts 16:7, not to mention Philippians 1:19, should have been translated as just Spirit, as opposed to Spirit of Jesus, the jury is still out on that one. From what I have been able to ascertain however, the 'latter' was in vogue in earlier MSS and was changed to the 'former' in later transcripts, probably to suit more trinitarian biased minds, would be my guess.
Just a short note on Numbers 22:23 and the expression the angel of the Lord. It is an established belief, at least among some circles, that Israel's guardian angel, who went before them during the 'Exodus', for instance, was a reference to Michael, the Archangel. Michael means 'who is like God' and this 'spiritual' personage of Michael could very well have been the 'pre-human' Jesus, but I fully understand that that belief is not for everyone. The donkey was impressed to the point of actually moving aside, even if Balaam wasn't.