1. Have a shower, blow dry your hair and put make up on with them in your care?
About 2/3 weeks for shower. Put kid on floor of bathroom, first in carrycot, then, later, in bouncy chair, then play gym. When they got to crawling stage, I made the bathroom baby safe, and put toys on floor and got on with it. If baby stood holding onto side of bath screaming, tough. (I don't blow dry hair or wear make-up). Shared baths were often easier once he was a toddler.
2. Regularly exercise?
Eldest 14 years, youngest 8. I swim whilst older kids are at a home ed class.
I did buy an exercise bike to use in the evenings after kids were in bed. That worked, except they used it as a climbing frame and broke it.
3. Eat a meal whilst they're awake without rushing it as you can't really spare the time?
Pre-weaning i sat happily and ate one handed whilst baby breast-fed. Once weaning started we moved onto family mealtimes, so not rushed, but not restful. Would sit baby at table in high chair and give him some fingerfood to throw about and I would shove some spoonfuls into each of us.
4. Watch a TV show you want to watch whilst they play independently?
Mine never played independently. So we would watch after they had gone to bed, but with the ability to pause every time they needed us. Then they get older and stop going to bed until the same time as you.
The TV now seems to belong to the kids, as does the laptop. I watch stuff on my phone. Usually whilst doing jobs such a cooking, ironing or sorting laundry.
You just need to find new ways to do things, and new ways of living.