Not wanting to do writing homework and throwing his pen or ripping up paper.
How do you respond to this? Is there any encouragement or do you go straight to punishment?
Not wanting to get out of the bath (shouting and kicking) so I end up just picking him out physically while he's wriggling.
Tbh that's common with lots of kids, again active encouraging rather then demeaning they obey may help. 'Come on dc, quick, lest get your dried and changed and go do something fun'
He seems to think this all funny.
He is 6, it is funny to him. He sees the situation through a 6 year olds eyes, not with the view of an adult with maturity.
Throwing something like a razor in the toilet and looking at me to see my reaction and thinking it's funny.
He shouldn't have access to razors! Throwing things in the toilet, not ok. You say he is looking for a reaction, it all sounds like your child is doing just that. How much do you give your child? If you just leave them to it and don't interact, play or encourage them your child will seek any response they can get.
He's also an embarrassment when I take him around friend's houses who have kids of a similar age.
This is a really odd thing to say about your own child tbh.
He poked his finger into one of their foam toys ruining it. When i ask him about it he denies it. He often lies and denies things which he has obviously done. When he doesn't get his own way he starts shouting etc.
He sounds like a kid who needs you. So many children tell lies because they haven't been steered in the right direction, or any direction, so so things to get attention but try to avoid getting into trouble at the same timeZ. It's almost like a call for help.
Other parents look at me like I can't control him and slightly shocked a his behaviour.
Other parents do this regardless of how children are behaving. You just have to look on Mumsnet to see how many people are out there judging others. You haven't been single out there!!