Don't forget people who are perfectly happy, not weighing up big decisions, wanting comfort due to a death of a loved one or anxious about something are unlikely to seek the services of a medium. The medium just needs to work out the issue and then they have their in and can go from there.
If they've not done advanced research, they don't go in with very specific information, they open you up with vague questions and narrow it down based on your reactions.
As others have said it's not rocket science to think mother plus grown up son equals a dead husband/father. If that was wrong then it's likely a grandfather has passed away at some point and they can switch to that. Person of a certain age likely to have a fairly traditional name, they guess the letter G, you react, they go with George or maybe Geoffrey as common traditional names that start with G. Also names tend to follow social class lines so there are clues from the family members in front of them.
If you are over 50, chances are you have a parent who has died. If you are young and it's a friend chances are some kind of accident as young people are less likely to die of a disease.
Man in uniform could be military, police, postal service, train conductor, a lot of professions wear uniforms, even more so in the past.
The most popular colour of car is silver/grey etc so chances are you have come into contact with one.
If you are a young woman, fairly good guess you might have a child and then 50:50 chance of getting the sex right. If they get it wrong are you going to go back and complain anyway.
I could say I am getting a letter or word coming through and your brain would automatically conjure up everything you associate with that word or letter because that's how brains work so you will be able to associate it with something.
Also to the poster above cause of death is listed on death certificates which are publicly available.
But if you believe in this you are going to believe and that belief is not coming from a place of logic, it's coming from a place of emotion and so no amount of explaining it will convince you. They prey on that, that's why people can spend thousands on them. You forget or write off the ones whose guesses were wrong and the ones who hit upon the right thing then seem even more believable.