Prayer fellowship
Concerning prayer with those who are not of the same denomination, I understand the WELS' position on fellowship and prayer. However, is it okay to pray with friends or colleagues who are not WELS members if I am leading the prayer? The same question goes for those who are still unbelievers, but are learning about God.
We are able to pray with people when we enjoy unity in doctrine. I would encourage you to have conversations with your friends or colleagues to compare their beliefs with biblical teachings. With church membership, people commit themselves to the doctrine and practice of their church. Your conversations with your friends or colleagues would likely reveal if they support and uphold false teachings or if the confession of faith they make with their membership and their personal confession of faith are at odds with one another.
When people are not united in doctrine, it does not matter who is leading the prayer. Such prayer is to be avoided. There are exceptions of course. For example, in my own home I can offer table prayers in the presence of others who may or may not join inwardly in what I say.
Your last scenario is different in that people have not committed themselves to the doctrine and practice of any church. More than that, they are interested in learning what Scripture teaches. Prayer with such people can be done.
Certainly, we can pray for anyone, and Scripture encourages us to do that (1 Timothy 2:1). Praying with people is a blessing and privilege Christians enjoy when they are united in faith. When people are not united in faith and pray or worship together, they overlook biblical fellowship principles.
There is much more than can be said about prayer fellowship. You may be interested in reading materials on the topic from the Wisconsin Lutheran Seminary Essay File.