Calculation wise, can it be said that TWR has all the cash flows compounded with the first cash flow, whereas MWR is an addition of separately compounding cash flows? Is this the only (calculative) difference between the two?

TWR is the return of the first dollar invested, removing the impact of cash flows in and out. MWR accounts for the sizing and timing of the cash flows. It is a better depiction of the investor’s experience vs TWR being a better depiction of the investment’s experience.

But the inflows are added in the calculation. BB3.

In TWR, you add back withdrawals only. Think logically. If you’re withdrawing money, that money was a part of the portfolio since inception and you’d add it back to get the true return generated within that period. Also withdrawal sign conventions are -ve since its cash outflow from account so be careful.

The BB3 example is perfectly solved. All end of period contributions are negated. No problem.