It’s good to be self aware and self critical but I think you’re over analysing yourself and putting negative labels on you.

A true psychopath wouldn’t care or have the ability to care.

The way you describe yourself you sound like you’re intelligent and insightful, and it’s unsurprising you would get on with older people if you’re more mature than others of your age.

You do need to be careful about inadvertently manipulating other people to your way of thinking - but anyone needs to be careful fit that, particularly if they’re skilled in being persuasive. Just because you can persuade people to your way of thinking does not mean you are always right. I’m able to do the same in real life but half to stop myself and think - it’s really important to learn to be open to other positions before you rush in and try to change people’s minds.

Having said all that, that is not “gaslighting”. You may need to understand what your friend is saying. It may be that actually you are doing a good thing in persuading them. Or it may be you’re inadvertently doing harm.

Or it may just be that your friend is very impressionable - some people are a bit like pillows - they will take on the opinion of the last person they spoke to much like a pillow takes an indent from the l last head they laid on. That’d be their problem, now yours.

Overall though, you seem to take quite a negative view of yourself or are worrying you are a “bad person” (although a psychopath isn’t bad, they’re just built differently; but obviously that seems bad to a lot of people). The fact you worry about being a psychopath shows you are not one, but also it shows you seem to be feel bad or guilty about who you are. You should explore why that is. As others have said, therapy can be a good way to do that. But having self awareness and a degree of self criticism (within limits) is alreadt a powerful thing.