With the fear that performing Ghusl harms her health, it is permissible for her to perform Tayammum.

No, it is not correct, as the sequence within tayammum is necessary. In order to correct the sequence, one can repeat wiping the hands after wiping the face.

Yes, it is necessary in validity of tayammum to make the intention to get closer to Almighty Allah.

Tayammum should be performed in the following method:
One should first strike the inside of his hands upon the earth once.
He should wipe, with both of his hands together, his forehead, and the two sides of his face from the place where the hair grows to the bone of the eyebrows.
He should wipe the back of the right hand from the wrist to the fingertips, with the inside of the left hand. Then he similarly wipes the back of the left hand with the inside of the right hand. It is best that he strikes the earth for a second time and then repeats the wiping of the two hands.

If he expects, although he may not be sure, to have sufficient time to offer the prayer completely in addition to performing the ghusl before it before sunrise, then he should do the ghusl and perform the prayer.
If he anticipates that he has sufficient time to offer part of the prayer only before dawn after performing ghusl, then as an obligatory precaution he should perform the ghusl and offer the prayer even if some of it is after sunrise.
If he realizes that he will not be able to offer any part of the prayer before sunrise, then it is better to perform the Tayammum and the prayer before sunrise, and then perform the Ghusl and repeat the prayer after sunrise.

If a person in the state of janabah fears that he will become ill if he does ghusl with water, then it is necessary for him to perform tayammum instead, in order to offer the prayers.

It is permissible to perform Tayammum with cement and plaster and the like of which originates from earth and then heated in fire.

It is not permissible to do Tayammum instead of Ghusl in the said cases as long as water is available. Our advice to you is to economize in spending water, avoid extravagance and perform Ghusl in a balanced way and without paying attention to doubts; having said that, using excessive amount of water in Ghusl does not invalidate it.

Tayammum instead of the ghusl of janabah compensates for the wudhu. If a minor occurrence, like sleeping or urinating, took place afterwards, and you can perform wudhu, then you must do so. If it is not possible, then you should perform the tayammum instead of wudhu for your prayers.

The tayammum becomes invalid with the elimination of the justification that caused one to perform tayammum. For example, if the patient who performed the tayammum instead of ghusl due to his illness was cured, then the tayammum is invalid immediately and ghusl will be required. The tayammum also becomes invalid also if the justification continued but the individual sustained another major occurrence (hadath akbar).

If the najasah is in the parts of the wudhu then one must perform tayammum instead.

If the time is sufficient to perform ghusl but the ghusl would cause harm to the body, then it is obligatory to switch to the tayammum. If the time is not sufficient to perform the ghusl and the ghusl would not harm the body, tayammum is not obligatory. One can perform the ghusl even if this leads to offering the prayer outside designated time of the prayer.

Tayammum in this case is not sufficient, as it is possible to perform the prayer in a different place, even if you perform it towards the end of its prescribed time. The leather is considered najis if it was not from an Islamic country but if you were living in an Islamic country, then the leather is considered to be tahir.

If the patch can be removed during the ghusl time, then one should do so and wash the skin underneath the patch directly. If this is not possible, you should wipe the water over the patch in ghusl, and tayammum should be performed as well.