You can see when they buy or sell a position. It's on the blockchain so it's all public. And yes, copying positions is called copy-trading and it's extremely popular.
Orders aren't public though. Only the actual trades. This is important because by the time the trade is known by others very often the edge is gone. Especially if you have other people watching the same trader and they all try to copy the trade at the same time.
If it takes so long for the actual trades to show up then why is copy-trading popular?
Not all strategies are low-latency, so you can copy trade someone with a buy and hold approach. For example someone you think is an insider or whale who might influence the outcome.