Is a patient who needs to take blood-thinning medications and refrains from eating or drinking certain foods and liquids required to fast?

Allah the Almighty has permitted a sick person who is harmed by fasting to break their fast, if fasting increases their illness, prolongs it, or makes it difficult for them. The illness that permits breaking the fast is a severe one that worsens with fasting or is feared to delay recovery.

Therefore, if you predominantly believe that fasting will cause you harm, due to the resulting changes in medication times, and the fact that this leads to complications, and your doctor has asked you to drink large quantities of water, then you must break your fast, and there is no sin upon you.

And as long as your illness is chronic and not expected to cease, there is no need for you to make up the fasts (qada'), but you must pay the fidyah, which is feeding one poor person for each day, a "mudd" of food (approximately 750 grams of rice or similar).