The US schooling system seems very different from the UK one! In a nutshell, the school year runs from 1st September-31st August (although there is obviously a summer break, usually from mid-late July until beginning September, although Scottish schools break up and go back earlier).
Most children start nursery (preschool?) here during the school year they will turn 4, so they could be anything from only just 3 years to nearly 4 years when they start. This year is a short school day and is all about preparing them for school by socialising them. There is no obligation to send them during this year, but many parents do as the nurseries are often attached to the schools and there is a larger chance of getting them in to the school if they have attended the nursery.
'Reception' year is for children who will turn 5 during the school year, so again, anything from just-4 to nearly-5; parents have a legal obligation to ensure that their child is receiving an education by the school term after they have turned 5, whether this is done by sending them to school or by home educating. A child who turns 5 in the term at the very end of the school year and whose parents choose not to send him/her until they have to, will therefore start the next term by going straight into Y1 (missing Reception altogether) unless there is a specific reason to be kept down. Similarly, children tend to stay with their own year group unless there are exceptional circumstances.
During the Reception year, the children do a lot of play-based learning, but they also learn to read using synthetic phonics. My younger son who was 5 in March has just finished his Reception year, and can read simple books.
Y1 (ages 6-7) and Y2 (ages 7-8) are Key Stage 1, and Years 3-6 are Key Stage 2, with this being the end of Primary school (aged 10-11).
Obviously, in the earlier years, the children who are young for their school year may be at a disadvantage, but the teachers all provide differentiated work for the children, according to their needs, and teaching assistants will often work with small groups of children within the class of 30.
It sounds to me like your son is ready in many ways, and as far as the dressing himself goes, being with a group of children who are doing things for themselves may spur him onto being independent. On the other hand, if you are really concerned that he isn't ready, you should trust your instincts. It is worth finding out what they do in Kindergarten, what age range they will have next year, and speak to his Pre-K teacher again to ask why she thinks he is ready.
S x