Arrive (where?) without any proposition
I'll arrive home at 10 pm

Arrive home звучит естественней, но люди до сих пор этот вопрос обсуждают. Я бы сказал 'get home'. Так оно вернее
https://www.italki.com/question/305575?hl=ru

Yes, "arrive home" is correct, but the explanation "arrive (where?) without any proposition" makes no sense.
Arrive TO work
Arrive TO school

in this case the right answer woud be just: I will arrive home,just because 'home' with the verb of movement is used mostly without an article at all.but if you say:I am at home or I left smth at home, here you should write the article, but it is not such estrict..

Useful note, Anton, on movement vs location. Just a minor error: at is not an article, it's a preposition👍

arrive to - типичная ошибка, которую любят вставлять в Toefl/Gmat
http://dictionary.cambridge.org/ru/%D0%B3%D1%80%D0%B0%D0%BC%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%B1%D1%80%D0%B8%D1%82%D0%B0%D0%BD%D1%81%D0%BA%D0%B0%D1%8F-%D0%B3%D1%80%D0%B0%D0%BC%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/common-verbs/arrive
Если вы приехали в чужой дом, то вопрос не стоит: "Arrived at their home". Почему в свой дом - без предлога? Возможно потому, что в "I arrived home" home - не существительное, а выполняет роль наречия места (adverb).

Согласен - как наречие. 'When I'm in town' - in town тоже в функции наречия, так как без артикля

The right way would be "I arrived home" or
I am at home. (static)
I went home. (dynamic)

Arriving is an action, so you do not use a preposition.