Is not the higher mind the first plane above our mind?
That is right. It is the first of the planes above the ordinary human mind.
Is the forehead (inner mind centre) a part of the higher mind?
No, it indicates the mind generally. The higher mind is above.
What is characteristic of the higher mind?
It is a mind of thought and knowledge and spiritual perception but spontaneously seeing the truth.
Could one cross the higher planes without establishing peace and silence? If so, would one feel the vibrations?
I do not see how it can be done without peace and silence, if it is the higher planes which are spoken of. Of course large mental and vital planes can be reached without it and in that passage there may be vibrations.
A few days back you wrote: “It happens sometimes when the force is flowing down from the Brahmarandhra.” What does this Sanskrit word indicate?
The place at the top of the head (called crown of the head) which is supposed to be the part at which things ordinarily come in from above and go out. E.g. it is through this that the being in the sukshma deha (subtle physical) goes out at the time of death and also it is the passage of connection (previous to opening) between the higher and the lower consciousness.
There are stories in the old scriptures, Puranas, that some great yogis were tempted by the Apsaras (fairies of other worlds). Then some of them left their yogic tapasya and even married them. Are these really facts or mere religious fables?
These things are possible but they do not usually happen — because it is difficult for beings of the subtle worlds to materialise to such an extent or for a long time. They prefer to act by influencing human beings, using them as instruments or taking possession of a human mind and body.