Runs test shows the randomness of your observations.

To detect monotonic trends: split data into 2 parts, compare frequencies using the binomial test.

Is there a way to reach you? I'd like to discuss this with you as per your convenient time.

Dipen Piyush Modi : Sure, you can pm me or write your questions here.

No because this is not least squares. It is a linear statistical model so that those assumptions should hold but the normality ols assumption does not. See Kutner et al, Applied Linear Statistical Models. Best, D. Booth