解答

1) Takuya seems [to be) busy with his homework. = It seems(現在) that Takuya is(現在) busy with his homework.
2) Rei seems(現在) [to have received](不定詞・完了形) a letter from Ryo. = It seems(現在) that Rei received(過去) a letter Ryo.
3) Ken seemed(過去) [to live] with his grandfather. = It seemed(過去) that Ken lived(過去) with his grandfather.
※[to be living]:不定詞・進行形 も可能。但し、それは祖父との生活が一時的で短期間であると分かっている場合。
= It seemed that Ken was living with his grandfather.

参考にしてください。

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