In the UK, we don't use "kindergarten". I think the direct equivalent would be "reception" class, but you could also use "preschool" or even "nursery" (this is what we called it in my part of the country but I'm aware in other places it's only used for the place where younger children (1-3 years) might go).
3-6 – but it is only a real requirement to attend „zerówka” as a preparation to school. „Zerówka” is for 6 year olds and 99.9% of them are part of „przedszkole”.
For children 0-3 there is also „żłobek” but that's simply child care(day care), nothing more.
Side note: „pomyśleć” is a perfective verb, so it doesn't work with „zawsze”, accusative of „lata” is „lata”, so: „Zawsze myślałam, że dzieci chodzą do przedszkola gdy mają cztery lata”.
If there isn't, there isn't. "Przedszkole" definitely isn't a primary school.
My advice would be to remember the simplest translations:
przedszkole = kindergarten
szkoła podstawowa / podstawówka = primary/elementary school
gimnazjum (non-existent now) = middle school
liceum = high school
It seems to me that this really is simpler than comparing the Polish school system to your own country's school system.
in the us kindergarten is most likely in the primary school, and is only for ages 5-6. Preschool or nursery school (more rarely used in US) would be for ages 2-5 and is usually separate from primary school. Sometimes some preschools go up to age 6 and include kindergarten for the oldest group. I think przedszkoła would probably be best translated as preschool for americans--is that correct? And then zerowka would be like our kindergarten?
As far as I know and quickly checked, it should be "attends (the) kindergarten", "attend to" means something slightly different.
(quote from some language learning forum: "I would say: 'you attend school'. 'to attend to something' is used when you take care of/deal with something. You attend to work or you attend to a case/a matter etc.. you attend to children... but you don't attend TO school. (you don't deal with the school, you're just present during the lessons).")
But it wasn't accepted so far, so thanks.