okay, first of all, I'd say none of the scenarios you have described sound particularly bad by 2yo standards.
In fact, the first one with the wellies doesn't seem like misbehaving at all: he wants to be a big clever boy and do the work himself (surely a good thing) but can't quite manage his frustration so screams. Here I would try to help him tactfully while voicing his frustration for him "Yes, I can see that you get angry when you want to put your boots on but you nearly did it, just let's turn them round a little together, there we are- well done!"
If I am on the phone or distracted he throws things to get my attention. Annoying, but not terribly bad, I don't think: their ability to wait is still limited. I'd just remove breakables and accept that you may need to pay him some attention too.
shop scenario again sounds normal. I used to strap dd in the buggy before we got to the shop at that age, and then just let her scream if she wanted. Nothing to feel embarrassed about. In fact, I got quite good at working out where I would need to get her into the buggy so that her screaming fit would be receding by the time we got to the shop. (Good tip for getting screaming child into buggy: when they draw breath their stomach muscle relax- that's when you gently and quickly push their tummy so you can do the strap up).
- he wants to go on a big slide but can't climb up the stairs as it's for older children and then becomes hysterical when I remove him. Kicking and screaming etc.
could you help him up the steps? Or alternatively steer him away from the big slide in the first place if you don't want him going up it. Talk to him, distract him seem very excited about the fun he's going to have on the other slide.
Either way, sometimes kicking and screaming tantrums are going to happen.
if he drops his banana, he will scream and shout until I get him another one. I am doing it as quickly as I can but it's not fast enough for him.
Reminds me of a story dh tells about how he was on the train with our eldest when she burst into howls of despair. An older lady turned round and enquired in a stern fashion what the matter was, evidently thinking he was hurting her in some way. Dh explained patiently that "she's eaten her banana". Cue: sniggers from the lady sat next to her, who was clearly versed in the ways of 2yos. Try not to let this situation stress you out.
Toilet roll holder incident- first of all, I wouldn't go down the route of repeatedly telling a 2yo to do something and then punishing him when he didn't. And you really don't want to encourage him to use pinching! Better procedure ime would be to say "no, ds, we don't play with the toilet roll holder" and then take hold of his hands so he can't. And distract him by talking about something else. He will still learn that when mummy says no, that means he doesn't get to do it.
road safety If he is a runner, then he is also to little to remember to control that instinct at all times. I'd get reins. Or one of those backpacks with reins.Job done, stress over. He will be safe and you won't be having the endless battles. Try to sell them to him as a new accessory.
It sounds like you are having a rough time anyway, and 2yos (at least the strong-willed ones) are exhausting, but I really can't see anything in what you have described that suggests either that there is anything wrong with him or that you haven't disciplined him enough. Parenting is work in progress; he is very much in progress. Just hang in there.