To answer your one question, yes they can basically do anything. Each person has their own specialties though so she isn’t all powerful. Women can control air and water better, men can control earth and fire better. So where she can throw a few fireballs, she’d use much less energy and be able to do more damage and specific things by using air, like when she hurled bricks.
Current time magic users are actually obscenely weak compared to how they used to be, and how some will become. There are magic focus items that make them stronger, they can also link to become stronger. Past magic users were so powerful though that one of them could manhandle a group of twelve current ones linked together and using focus items. They leveled mountains and destroyed entire cities by themselves if they had a focus item.
Don’t worry too much about the samurai / Asian trope guy. His entire city is gone, he’s the last of his kind. His role is more of a personal guard (called a warder) to moiraine. All the different color aes Sedai have one except red. Greens can have more than one (And they fuck theirs too!). They’re from every land though, not his, so they don’t all act like him. The warders are linked to their aes sedai with magic and can always tell where they are, gain some abilities like faster healing, more energy, can sense where dark one creatures are. You saw a little of that in episode 1 when she asked him if an eyeless was nearby.
