We often say 今天下午你休息的好吗? If you say“今天下午你休息吗”, it sounds like you asking one to have a rest this afternoon. :D

下午休息的好吗？ 你下午休息的怎么样？ They're more normal in Chinese, and not so prolix, when you say 下午休息的好吗，we know you mean "Have you rested well this afternoon?"

今天下午你休息得好吗？ Chinese usually say “today” instead of “this” ，so it'd better to say 今天下午，eg this morning=今天上午，this year=今年， but when refering to this week or this month，we say 这个星期 or 本周；这个月 or 本月。

这个下午你休息得好吗? Here must be a "得". Like the "well" modifies the verb "rest", the 好 modifies 休息。It shows how good the rest is. If there isn't 得, the sentence will mean that you ask somebody to rest.