I am eager to know and understand whether or not there is any sort of relationship between fasting(either food or water) and karma? Does any scripture clearly states that fasting helps in eliminating/reducing/burning our karmas?
The following verse shows that fasting leads to accumulation of merit (Punya or good Karma).
Manu 2.188. He who performs the vow (of studentship) shall constantly subsist on alms, (but) not eat the food of one (person only); the subsistence of a student on begged food is declared to be equal (in merit) to fasting.
And verses like the ones given below show that fasting helps in destroying sins.
Manu 2.220. If the sun should rise or set while he is sleeping, be it (that he offended) intentionally or unintentionally, he shall fast during the (next) day, muttering (the Savitri)
11.166. Fasting during three (days and) nights shall be (the penance for stealing) grass, wood, trees, dry food, molasses, clothes, leather, and meat.
Fasting on auspicious days like Ekadashi and others also leads to removal of sins as per Puranas (as shown in answers like this - https://hinduism.stackexchange.com/a/8328/4732_).
Therefore, fasting, if done in the prescribed manner, helps in destroying bad Karmas (Papa) and in earning good Karmas (Punya).