Is S&P 500 a capped index, and is it a Total Return or a Price Return index?

The S&P 500 is only adjusted for special dividends, share buybacks, and other corporate actions (splits, mergers) so it is neither completely a price return or a total return index (although since the latter are more infrequent, it's closer to a price-return index).

When the companies within the index pay a dividend, the price of their shares (and thus the index) goes down.

Note that the index itself is just a number - it is not a fund or anything actually investible. Funds that track the S&P 500 (or any other index) by buying the component stocks in the same proportion as the index can choose whether or not to reinvest dividends, which is where the confusion may be coming in. There are versions of S&P 500 trackers that pay out dividends (and effectively are "price return" funds) or reinvest dividends for you (and are total return funds).

There is no cap on weight in the current index. It's a simple weighted (by number of shares) average with a divisor to account for corporate actions listed above, and to keep the index value consistent when switching companies in and out.