What is this type of person does it have a name?

[Vandalwatcher]

Someone who does see other people’s emotions separately, they relate it to their own feelings:

(and how do you coparent with such a person)

examples:

• someone is crying, upset or angry. They may comfort that person but somehow relate the upset to themselves and get upset about it so it becomes all about them

• Kids learn not to upset this person by expressing their own feelings

• they got cheated on years ago by someone else, so think their partner will do it too. They stop them from having opposite sex friends and constantly bring it up even if that person has done nothing wrong or untoward. Their partner can’t even watch the opposite sex on TV without comments

• They don’t seem to think about how their actions affect others ie being very late with no explanation or apology

• They forget everything like kids coats, shoes, kids not dressed appropriately for the weather.

• They make plans with the kids on the other parents time then expect the other parent to facilitate it

• They want the majority of access to the kids on special occasions and don’t reciprocate to the other parent and take turns or they agree too but then encroach on the other parents time

• they are never ready with the kids on time at the agreed pick up times

• They never spend time with their kids by themselves another adult is always present

• They prioritise the needs/feelings of a new partner over their kids needs/feelings

Narcissist, controlling, selfish are possible names that spring to mind.

Arsehole?

That is called a narcissist.

As far as co parenting with this person- it will never be easy. Grey rocking and having firm boundaries would be a good thing. Absolutely everything needs to be laid out.
Nothing you do will eliminate every problem but these things can help lessen the issues you will have.

Is this person aware that they are late/forgetful regarding the kids and do they want to get organised but can’t or do they not care?

I think these people like to call themselves "empaths" nowadays (certainly your first few points) but yes, narcissistic, selfish etc.

An ex.

Not clear it appears they don’t care but sometimes they do manage to do it.. if it suits them. If they have somewhere to be then they will be on time but they don’t worry about wasting someone else’s time