Cat behaviour - help!

[Tipsylizard]

I am looking for some advice please. We adopted a rescue cat about 3 months ago. He is 4 years old (approx), we don't have much of background but the shelter advised he would be good match for a family with young children. I have experience of cats when I was growing up but always from kittens.

When I took him to the vet they said it was likely he was neutered after adolescence due to his size. He was initially very nervous but then seemed to calm. We have a large house with a garden, near lost of green spaces. He has a chipped cat flap that he can use so he can come and go as he pleases. He has lots of places to go and hide/rest/sleep in peace. He is fed a mixture of wet and dry food.
He is seemingly very friendly/interactive but we are having problems with his behaviour.

He has scratched, bitten the children (4 and 2) a number of times - some of this is because he is feeling backed into a corner but sometimes he actively comes to where we are in the house eg. into the bathroom when bathing the kids and gets riled up.

He follows me about constantly. Waits for me outside the toilet even. When I work from home he literally tries to lie on my keyboard but he won't let me stroke him without scratching/biting. He stalks my legs when I walk away from him (not seriously but in a playful way - still hurts though). He does not do this to my husband. He constantly rubs himself against my legs. He won't let me pick him up but will come and lie next to me on the sofa purring. He has been overly affectionate with one particular blanket on more than one occasion. He stays out of our bedroom at night unless there is just one of us in there - then he is in the bed like a shot. Although he can go out whenever he likes, I don't think he does that much - although he could overnight. He also seems to be constantly looking for food but is definitely fed enough.

He never hisses or yowl so you don't get much warning - he can be purring then scratch.

I have tried to educate the children how to make sure they don't frighten him or get in his face but they are young and they are now scared of him and I can't leave their bedroom doors open and to be honest I don't like my legs getting attacked.

Sorry for the essay! Has anyone got any advice please?

It sounds to me he has lots of bent up energy and he's looking for company/stimulation a lot of the time. Are you having any high intensity play sessions with him, for example with a dangly feather toy to catch or a laser pointer to make him really run around?

When you say he scratches, do you mean he swipes, or that he is reaching and has his claws out (i.e. more unintentional than swiping)?

Definitely sounds like pent up energy. Try and get some big kicker toys and leave them around the house, when he wants stroking/fighting use them for him to attack instead of your hand. Do you have a cat tower? They are good for them to jump around on.
Is he satisfied with his food? Full enough? Mine can get really cranky when hungry.

Some cats are just dickheads tbh. I had a cat who was rescued, he must have been badly abused as even from a kitten he was horrible and would suddenly turn and attack. We got used to him and would find it easier to spot his warning signs and realised that all the affection he wanted had to be very much on his terms. Sometimes he would just want a quick 5 second head scratch and then would attack to say he’d had enough.
He calmed down as he got older and by the time he was around 8-10 he was much more laid back, although everything still had to be on his terms.

I know this can be hard to cope with with young children though as obviously you don’t want them to be hurt.