To know which exit strategy they are likely to use, you need to research the private equity firm and see how they have historically exited from their investments. Obviously, there is a chance that they don't follow a specific pattern and even if they do there is nothing preventing them from using a different strategy for your current company.
As to signs that one of these items is pending, being that you are a remote worker it would largely depend on your role at the company or who you know.
Depending on your role, you may receive unusual requests or notice uncommon audits related to your role. For example, if you are working in the IT side, they may want to do an unscheduled security posture check or penetration test ( assuming your company regularly performs these ). Maybe you work in the accounting or financial side and the PE begins asking for more than usual figures, forecasts,....etc.
The easiest way is if you know someone high in your company's hierarchy and have a good enough relationship where if they knew about some impending event they would have no issue mentioning or discussing with you.
Unfortunately, other than researching the PE yourself, the others will likely be mostly out of your control. Just do your job and try not to worry about it. Remember that the question isn't if the exit will happen, it's when.