Just only a small thing that you are in doubt "nasai", it is equivalent to the English word " please". By definition, it works with the verbs +nasai,
all words in Japanese have the stem, you need to chance it to rule (2)
"kaeri" it is wrong by itself, it's stem is "ru". So, the correct word by itself is kaeru. In conjugation, the rule for "ru" is (1)ら, (2)り, (3)る, (4)る, (5)れ, (6)れ. In rule 2, it is change the stem from るto り.
oyasuminasai, yasumi is wrong by itself, it's stem is む. yasumu (休む). The conjugation rule for む is (1)ま, (2)み, (3) む, (4) む, (5)め, (6)め.
"O" is not related to the verb yasumu, just for being more polite.