Yes I agree that cap weighting doesn't over buy the low P/E stocks.
I'm not sure I agree that low P/E means that a stock is undervalued. For example a company that is guaranteed to make $10 every year should probably have a higher P/E than a company that is expected to make $10 with $1 variance.
If we move to a more abstract notion of undervalued then I still agree with you that cap-weighting isn't guaranteed to overweight the undervalued stocks.
Sorry, you're totally right. The prices should increase in the same weighting when buying just like they go down in the same when selling.
The difference is that you're weighted by market caps, so you're increasing the P/E of the entire market (in a super small way). That is, you're not investing more in companies that are valued more "attractively" (lower P/E multiple) than those that might be "over valued" (high P/E), which is what the market typically does to determine prices.