Translation:I have been busy recently.
Both are pronounced "Kaishi". Japanese doesn't have the tones that Mandarin does, and with many characters the Japanese lifted from Chinese, they took the pronunciations from a different, much older dialect of Chinese. However, in Mandarin, some of them stayed the same, and 開始 is one of them.
Referring to something in the past that applies up to the present requires the present perfect tense in English in order to be grammatically correct, irrespective of the source language. The use of 最近 is a reference to the past. (The correct answer at the top now uses the correct tense).