Vehicle tyre fitting generally takes 30-60 minutes for two tyres and 45-90 minutes for all four. The fitter mounts the tyre, sets the pressure, and balances the wheels. It usually takes less time if customers show up at the scheduled time.
The fit time does depend on stock availability and the workloads of the local fitters. Searching by registration and selecting the first time slot will result in the fastest tyre fit.
Run flat tyres need special type wheels. They also need specialised equipment to fit them. Make sure to check the marking on your tyres. Only use them if your vehicle uses run flat tyres.
If you have a tyre that is losing pressure, inflate it and check it again after 24 hours Then you can drive safely and not have to worry about fast long distance driving. Many tread punctures can be repaired, but sidewall damage means the tyre must be replaced. Make sure to get it checked as it's a safety concern.
While alignment isn't strictly necessary, uneven wear, pulling in the steering, or if the wheel is off centre should prompt the consideration of an alignment. Alignment should also be done to protect the life of the tyres and the brakes as lack of alignment can affect both of those systems. Alignment is a good add-on after hitting a few potholes.