what being apart from the law means.

[Drich]

I think this falls within the "Total Depravity" doctrine. I think that doctrine is incorrect.

Not familiar with that one.

Throughout the Word people are called upon to repent.

without a doubt repentance is an absolute must, but again can not happen if the potential believer does not see anything wrong with how he lives his life.
Even in the bible (NT) the Call to repentance is only ever issued to one looking to be right with God. (The Pharisees on mass did not receive such a call)

Take the example of John the Baptist. He called on people first to repent and then afterwards they received the Holy Spirit. The dove landed on Jesus after he was baptized, not before.

One could argue this was well before the out pouring of the Holy Spirit in Acts 2.

For after this out pouring of the Holy Spirit we have examples of the Holy Spirit interacting with people before and after they were baptised. In Acts 8 starting at verse 14 you have an example where as you said people had been baptized and did not receive the Holy Spirit (until peter laid on his hands.) In Acts 10 The Holy Spirit was poured out onto a Crowd (that even included Gentiles) and were not baptized till after all of this had taken place.
44 While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. 45 And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. 46 For they heard them speak with tongues and magnify God.

Then Peter answered, 47 “Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?” 48 And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days.

What Christ is calling for in Luke 11 is similar to what happened in this accounting of Spiritual outpouring. For the Gentiles would have never even have been considered for salvation till the Spirit inspired them to act.

Repentance is a step everyone has to make on their own of their own freewill and accord. If the Holy Spirit makes us convert that undermines our freewill.

No one said the Spirit makes us do anything. I very clearly stated that the Spirit simply makes us aware of sin. (to the point where we can not reason it away.)
Then it is up to us to repent of said sin. If we do we will be given a larger portion of the Spirit and if we don't what we have will be taken away and given to someone else.

Now if all you are saying is that people have to recognize their sins and be prepared to receive the Holy Spirit, that's fine. But we both know that the Spirit works through the Word, so reading the Bible and learning about what sin is should be enough for people to feel convicted if they take what it says seriously.

Which falls under the "seeking" portion of what Christ told us to do.