Selling on several channels works when stock, prices and reporting follow one set of rules.

How should stock be split between channels?

By the economics of each channel: its fees, fulfilment cost, margin per unit and demand pattern. The rule is set once and applied to every order, because deciding by hand, order by order, gets slower and less reliable as volume grows.

Should prices be the same on every channel?

Not necessarily. Fees, fulfilment and buyer expectations differ, so different prices can be justified as long as each keeps a minimum margin and none undercuts the distributors who carry the product.

Who should own the price list across channels?

One person, usually from sales or commercial management, who keeps a single price list with a floor for each channel and signs off every change to it. Whoever runs each channel can then plan promotions inside those floors without asking each time.

How do you keep promotions from colliding across channels?

Plan them on one calendar every channel can see, and keep each discount above that channel's price floor. A promotion in your own shop can make a distributor or your Amazon offer look expensive, so it is checked against the other channels before it runs.