Are the Karmas stored in our minds or are they stored somewhere remote? Are Karmas relative or are they absolute? (In the sense, is good Karma or bad Karma defined?)
No its not exactly in the mind but the Karmas are attached nonetheless to the Jiva till it attains liberation. So, its also not somewhere remote. (However, if you take into account Chitragupta keeping an account of our Karmas, then it's somewhere remote).
Devi Bhagavatam 7.30 says:
The Karma, auspicious and inauspicious, done in many previous lives and preserved in seed forms, remains always inherent in a human soul. Urged on by this Karma, the Jîvas quitting their previous bodies, enjoy Heaven or Hell as effects of these, their own acts. 22-23. According to their good or bad works, the Jîvas acquire the higher happy body and enjoy various pleasures in the Heavens, or they take up very painful vicious bodies and suffer various pains in hell. 24-25. At the expiry of the above period in Heaven or Hell, when there comes the time of his assuming another body, the Jîva becomes conscious of the subtle body (Linga Deha) and takes his birth again. When the Linga Deha comes into existence, the part of the Karma done in various previous births that are ripe and ready to yield their fruits, gets attached to the Jîva by God (or Destiny).
From this passage it is clear that the imprints of Karmas are carried by the Jiva on it's subtle body which is known as the Linga Deha.
Karmas are not destroyed unless the Jiva attains Moksha. Same is the case with this Linga Deha. It is also not destroyed until liberation happens.
Sukshma linga sharirAntadA mokshadakshayam priye ||
O Beloved! The subtle body or the Linga Sharira exists till liberation.
KulArnava Tantram 1.11
Therefore, it is fair to state that its in the Linga Deha the Karmas are stored.
But you should note that the mind is also one of the components of this Linga Sarira.
Vedanta Sara Sutra 62 says that the Linga Sarira is composed of 17 components of which mind is one:
AvayavAh tu jyAnendriya panchakam buddhi manasi karmendriya panchakam vAyu panchakam cha iti ||
The five organs of knowledge, the five organs of actions, the five vital airs, mind and Buddhi -------- these 17 avayavas constitute the subtle body.