It sounds like you are doing great. Don’t worry, do your best and reflect on what can be improved. Ask your boss as the salon may have guidelines for dealing with some of these issues.
for instance late arrivals - in my salon we suck it up if they are 5-10 minutes late but after 15 minutes we adjust their treatment - a file and shape instead of a full mani, regular polish instead of gel - if I have another client. If I don’t then I tell my client that fortunately I have a gap so I can still accommodate their booking, because it’s awful after rushing and paying for car parking to then be turned away - and we hate keeping deposits. That usually makes clients thoughtful and they try a bit harder to arrive on time in future. But this is my salon rules, other businesses may have a different policy,
if you run late though, you can’t expect clients to be punctual. It goes both ways. If you’ve kept a client waiting in the past they’ll feel it’s only fair if they swan in 15 minutes late and they’ll be surprised to find you are waiting for them!
other advice I can share is to take the time to be organised. If you clean up as you go, so that your client isn’t surrounded by mess when she leaves will help you turn around for the next client. And have a place for everything, if you can put your hand in whatever you need it’s so much easier. Faffing about picking up bottles to find the top coat, or rooting around for a clean nail wipe make you feel stressed and wastes time.
Not having time for indecisive clients who change their mind is a good thing! It shows you are in demand so feel proud as well as sympathetic. Talk enthusiastically about next time and carry on with the treatment they booked.
Finally work on organising your clients. Ask them if they need to use the loo to make themselves comfortable when they arrive andask if they’ve thought about colours as you show them to their seat, set yourself up for rebooking during their appointment by asking if they want to return in two weeks or three, is the day of their appointment a good day of the week and would they like a similar time? When you take their payment you can quickly check for availability and swiftly narrow down the options to offer them.