Thank you for your important question.
May Allah, Most High, reward you for your desire to increase in knowledge.
It is permissible to write and take short notes in a copy of the Quran.
(Ibn Humam, Fath al-Qadir)
As for pens that contain alcohol in their ink, it depends on the alcohol. Many pens are made with Isopropyl alcohol which is pure due to it being synthetic.
Some pens are made with ethyl alcohol. If the ethyl alcohol is derived from anything other than dates and grapes, it is pure and permissible to use when writing in the Quran.
The majority of pens have alcohol that is not derived from dates and grapes.
And Allah alone knows best,
[Ustadh] Omar Popal
Checked and Approved by Shaykh Faraz Rabbani