I don't feel anything when people call me either of those things. But I do think people who don't work on forensics or criminology should not refer to anyone as psychopaths/"sociopaths."

Besides it being childish to just call someone a psychopath simply because they treated you badly or because you don't think they act right morally, it does affect negatively on people who do have ASPD. There's people out there who are trying to be "good". Always painting them like they're Irredeemable might deter someone from getting therapy. If people will still treat you like a monster over your disorder no matter what then what's the point of getting better? "I will be treated badly, so why would I try to treat people with kindness? Why control my destructive symptoms?"

I think this is something you should ask more than one PwASPD. Aspd is a complex disorder and the symptoms vary for each person.
Again, you should use the DSM-5-TR as your base. (Even if there's some Criticisms to be made about the diagnostic criteria)

It's always important to remember pwASPD have traits outside their disorder, things they like and enjoy, etc.
Some of the symptoms of ASPD are impulsivity, irresponsibility, irritability, lack of remorse and empathy. Some people's symptoms are more obvious to the general eye, they have a harder time controlling their impulsivity. Then there's people on the other side of the spectrum, their symptoms aren't obvious/they "mask", but they're still present and affect them to some degree on their daily life (it wouldn't be a disorder if it didn't!)

There's some thoughts associated with ASPD, they can't love or feel genuine care for other people but themselves, which is true for some! But This isn't the case for many pwASPD. (None of these makes them "less") Keep in mind that love and care might look very different for someone with ASPD. Again, i would suggest you to ask more users with this disorder to understand how that works for them.

Many of the symptoms of ASPD are there to protect the person, the lack of empathy, manipulation and lying are there to help the person survive. Most of these people were neglected and abused as children, and they found the only way they could survive was through lying and manipulating. Empathy and remorse aren't useful when you're constantly fighting to survive.
So keep that in mind when you're writing a character with ASPD, although sometimes a person already has that lack of empathy and remorse as a child, so... there's that. (It's specially common if there's evidence of this disorder existing in the family)

Empathy may vary, sometimes you have a complete lack of empathy, sometines it's limited/low. The same can be said for remorse.

Drug use/abuse is common, the "main" reason behind this is the chronic boredom people experience with this disorder. because of said intense chronic boredom, they may seek thrill in many ways.

Anyways, this is very short. even if I experience many symptoms of this disorder, I'm not a know-it-all. There's a lot that can be said about this disorder that I'm simply too tired to write down (or I simply don't know). I'm not the ASPD lord so that's why I suggested you to go to more pwASPD. Good luck