Shopped orders - yes - who they are no. It's a much deeper question about ISOs and desk markets and the answer there, is it all depends on the product and visible liquidity. A much deeper issue and dark liquidity plays a big role.
A private trader has an enormous advantage over an institutional trader because of size. I can get my entire account into and out of the market in less than two seconds. Large institutions may take hours or even days to establish a meaningful position. In the days of pit trading it was possible to see what the large institutions were doing because everyone knew who their brokers were. That is no longer possible with electronic trading. However knowing whether a large institution is buying or selling is not necessarily useful. They are not always right and one doesn't know why they are buying or selling. They may be buying futures as a partial hedge to a short cash position, so they really expected the market to go down. Institutions employ skilled traders who don't use dumb systems, or automate something based on a couple of moving averages and an indicator. Is also often the case that the guy or gal doing the buying and selling did not make the decision to buy or sell, that came from a portfolio manager. The traders job is to get the best price possible. It is much better to be a private trader.
I guess all that are available in the particular brokerage company. btw you can claim a special offer (being an institutional trader) or smth of the kind