Hi,
Starting with the batting, each shot seems to be pre-meditated and rushed due to the amount of movement you do prior to even beginning the lift of the bat- which highlights your hesitancy at the crease that may be down to your fear of getting one in the chest. Furthermore, being so busy around the crease is not the worst thing in the world but while you are moving significantly all over the place it reduces your reactive ability to the pitch and line of the ball (thus resulting in some of the nick-offs). In the second shot that you play, you can notice a significant 'bounce' just after you play the shot which is primarily down to an excess amount of force as you drop into the cover drive. This is as you have swung through the shot without coordinating the whole of your bodily motion to commence at the same time, ending up with your body playing catch up on itself to maintain balance by dropping the back leg quicker. On the other hand it is then the opposite way round when you attempt the sweep, by lowering your centre of mass you become more balanced. However, now your arms are playing catch up because you have pre-emptively gone for a shot. I reckon that your back probably hurt a tiny bit when your arms swung through and then after reaching its point of bind it pinged back slightly which made you off balance. What i would suggest for the coordination is probably, without the bat initially just attempt to pad the ball and get your hands moving in time with the plantation of your front foot towards the ball. Then borrow a really light bat so that you have to focus more on coordinating correctly and controlling the bat speed as you go through, by doing so you will slowly adapt to playing through each shot slower in relation to the bat. Once you are able to play the shots within the V with control, you will notice that the shot power will come with how you are able to control each shot.
On your point about cuts, pulls etc. Start with (not being patronising) a incrediball being thrown underarm towards your mid section to build your confidence with each shot. What you are looking to achieve for the flicks are to make room by your hip so that you can just guide the ball down the leg side. Cuts you should be moving your right foot back and across towards the line of the ball, and with the pull shots, look towards moving like you would with the cut but less so to get the ball in line with your head so that you can play the ball on the leg side and watch the ball all the way onto the bat, it seems basic but by getting a solid foundation allows you to build up your skill set back to what it formally was.
Bowling-wise, your run-up is more of a stutter affecting your stride length and frequency that affects your acceleration substantially and as said previously you're trying to go from 0-100 in half a yard

but you should realistically build up your pace as you get to the end of your action. The follow through from your action shows that your motion isn't fulfilled i.e. you have still got more force to exert in the bowling action. Rather than worrying about your mates work out a paced out distance that you feel allows you to reach your quickest before getting into the bowling action... Following which, then look at your front foot directing straight down the track because in some instances in the videos it ends up pointing towards second slip which means you aren't transferring your force linearly down the track that translates into additional pace.
Sorry for the very science'y approach but being a scholar it makes things easier to explain. Hope it helped in some way, shape or form!!