“A company’s income appears directly on the I.S. and the R.E. statement, and it is included indirectly in the company’s B.S". Do you agree?

Yes.
Net Income is the bottom line figure of Income Statement and this Net Income is transferred to Retained Earning Statement for necessary adjustments.
The bottom line figure of Retained Earning Statement is the Ending Balance of Retained Earnings, a part of Capital.
Since, Capital is reported in the Balance Sheet; it indirectly includes the Net Income reported by the Income Statement.

Agreed.Income has been accumulated in the company's assets that is one of the reason of positive change in BS assets without change in liability and it goes to Retained earning.