My understanding is that elevated uric acid is a marker for metabolic damage (as is type 2) and that homocysteine is a marker for inflammation and much linked to heart disease and vascular issues (stroke, dementia).
Since inflammation promotes cell proliferation at the expense of excess vitamins leading to hyperhomocysteinemia, therefore, homocysteine can be used as a marker of inflammation to indicate the presence of inflammation.
Excess purine containing foods (not beans) were thought to lead to excess uric acid in the past when the richer part of the populations suffered gout and it was observed that these people at red met and drank port and the crystals that result in painful joints but a with all things nutritional it is hard to unpick what causes it but yet again excess insulin (insulin resistance) and kidneys holding onto too much fluid is supposed to relate to this condition too.