The only real fix is to drive more, and you may as well start doing that now. If you know the roads where you live you're better practicing there and getting some more hours behind the wheel before you move somewhere new with totally new roads. As others have said, take someone calm with you who isn't going to shout at you if you get something wrong. Also going out early in the morning is good for quiet roads, especially on a Sunday.
"I cut someone up on the mini roundabout today because I misjudged how far away they were from me. They sounded the horn at me which made me scared."
Not ideal, but just highlights that you need more road time to build up your experience and perception of other road users.
"Yesterday I switched from the right hand lane to the left hand lane when exiting a roundabout. There was no car behind me but the passenger said if there was this could have been an accident"
This is something a lot of people do but shouldn't. It's not against the law as it's a legal lane change, but it's a bad place to attempt one. Part of driving is realising where you've messed up and learning from it. Now you know to wait once you've taken a two lane exit on a roundabout until you're a little further down the road to change lanes.
"The day before I didn't see a zebra crossing and there was a cyclist waiting to cross but I didn't see him at all until after I'd crossed and the passenger pointed it out. Thankfully he must have seen that I was coming too fast and he waited instead of crossing."
If you read the highway code again you'll notice that pedestrians don't actually have right of way at a zebra crossing until they've stepped into the road. If they're just waiting on the pavement then you have no legal obligation to stop for them, it's just polite (and good to slow down in case they do step out in front of you). I hope the cyclist was walking their bike because it's an offence in itself to ride a bike across a zebra crossing.. The main bad point is that you actually missed the zebra crossing in the first place, but if you're still not very confident I imagine you were suffering from a little mental fatigue.
The only way to fix it is to drive more. Driiiiiiiivvvvveeeeeeeeeeee