If you pick stocks with the correct weight to track the index, you're effectively running an index fund. And so you don't have to rebalance to keep tracking the index.
You can add stocks whenever you put money in. Whether that's because you got your paycheck or a dividend or some other income is kind of irrelevant. And you can remove stocks when you take money out. But you probably shouldn't start selling one stock to buy another just because their prices moved, unless you have information that lets you time the market.
But then you wind up with a portfolio that isn't balanced and isn't tracking like an index fund. An index fund doesn't simply buy a flat amount of stock and hold it, they buy stock in proportion to the relative weight of the exchange. Which is always moving
Market cap weighting is special. If company A has 500 shares, company B 500 also, than a fund that has 5 shares of A and 5 of B is market cap weighted.
And what happens if company A issues more stock? Company B is delisted? Company C is now listed? Company A and C merge? Company A spins off it's most valuable side business into it's own independent listing company?
500 shares of company A is worth 100% of the market cap of company A.
500 shares of company B is also worth 100% of the market cap of company B.
So if you have 5 shares of each, you'll have 1% of the market cap of each, even if one of those companies finds the cure for cancer or turns out to be a money furnace.
What are you talking about? Those index fund are constantly rebalancing. This is why you buy an index fund, so you don’t have to constantly rebalance your portfolio.
2 You need to rebalance to take corporate events into account: new stocks, buybacks, dividends, etc...