Yes, kids at about this age, wait until the last minute, and have accidents. They simply "think" they can wait... and are busy playing perhaps, but then they can't wait..and thus accidents.
Don't feel this is only your child. Tis' the age. Even my daughter's preschool and Kinder Teachers say this. It is a though, yes they are potty competent... but then they get at this phase where they "think" they can hold it forever and ... but simply can't. Then they have an accident.
About wiping themselves: yes, in school they can do it and have to. At home, they like to feel cleaner... thus M. helps wiping. But at 4 years old, I really don't think they have totally great coordination to wipe completely and well... and they often times still have skid marks on their undies. Yes, at home, I say in terms of my daughter... as she got older she can wipe better AND cleaner, with no remnants. But... until last year, when my daughter was 6 going on 7, is when SHE could wipe COMPLETELY cleanly. And... after commiserating with my friends, they have said the same thing about their kids and wiping.
At least for me, my daughter was real stoked when she could wipe cleanly and feel clean after. And, I often did help her, because I did not want her having an unclean bottom... which for girls is even more important because they can get UTI's. Or, I would have her wipe... then I would check her after, to make sure she did do it, cleanly.
Anway, I think at 4.5, they "can" wipe.. but it will not be perfect, nor perfectly absolutely clean. I don't think a 4 year old will wipe until the toilet paper is "clean." Which is how I teach my daughter about knowing "when" to wipe until....
All the best,
Susan