Does the Bible teach us that Jesus placed a higher importance on Spiritual family above physical family?
He placed a higher importance upon God, which is why He seemingly berates the physical family. People who are not in your physical family become as though they were when united in Christ. So more are included but that doesn't mean your literal family is excluded from your love, devotion, etc.
What should be our heart concerning unsaved physical family, having communication with them?
Obviously I don't know your circumstances but as general guidelines we should have love, brokenness, servant-hearts, humility, a longing to steer them to Christ, etc. Definitely have communication with them. Pauls says,
"I wrote to you in my epistle not to keep company with sexually immoral people. 10 Yet I certainly did not mean with the sexually immoral people of this world, or with the covetous, or extortioners, or idolaters, since then you would need to go out of the world." 1 Cor. 5:9-10
and again
"10 Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. 11 But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife.
12 But to the rest I, not the Lord, say: If any brother has a wife who does not believe, and she is willing to live with him, let him not divorce her. 13 And a woman who has a husband who does not believe, if he is willing to live with her, let her not divorce him. 14 For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy. 15 But if the unbeliever departs, let him depart; a brother or a sister is not under bondage in such cases. But God has called us to peace. 16 For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife?" 1 Cor. 7:10-16
(This is clearly about marriage but I think the heart of God is displayed on the matter of families. As much as depends upon the believer stay in the relationship in order to bring that person to Christ. And realize that your presence is God's grace at work in those people's lives.)
Is there such a thing as Physical family idolatry?
Of course, only because this threat exists with anything other than God Himself.
As for those verses (Matthew 10:34-39, Matthew 19:27-30, Mark 3:31-35, Mark 10:28-30), remember the same Jesus cared enough about His physical mother to declare upon the cross:
"25 Now there stood by the cross of Jesus His mother, and His mother’s sister, Mary the wife of Clopas, and Mary Magdalene. 26 When Jesus therefore saw His mother, and the disciple whom He loved standing by, He said to His mother, “Woman, behold your son!” 27 Then He said to the disciple, “Behold your mother!” And from that hour that disciple took her to his own home." Jn. 19:25-27
Again, these things I am submitting to you are just broad themes. I don't know the exact situations and heart from whence your questions arise. You will have to seek the Lord and guidance from one you can wholly disclose and confide in.
God bless you in this season.