“时不时”和“断断续续”经常在一起用，但是感觉“时不时”貌似是说“有时下，有时不下。”，“断断续续”是“下了一会儿，停了，又下了，又停了。。。”这种感觉。个人觉得“ on and off ”可能用“断断续续”更好一点。我在网上查了一下，“时不时”对应的英文是 now and then .应该和 on and off 侧重不同

It's been raining on and off all day (Indicating it is still raining/you expect it to continue).

今天时不时地下着雨 今天一直在断断续续地下着雨

It rained on and off today (Indicating, the day is over and it has stopped raining) 今天断断续续地下了雨   这个句子很贴切！但是好像不常用。

It rained on and off all day today (Indicating it has stopped raining with an emphasis on 'all day') .雨断断续续地下了今天整整一天。“整整一天”和 “一整天”让人觉得从早到晚（all day）都在这样断断续续地下雨，而且“今天已经快结束了”。“整整一天”语气更重一点

It's been raining on and off all night. (Indicating it is still raining/you expect it to continue) 今晚咝咝啦啦地下着雨  左边有一个“口”，拟声词（onomatopoetic word）一般都有这个“口”。（但是“汪”没有。是狗的叫声，还可以做形容词，比如说人眼睛“泪汪汪”）就是说，下雨的声音听上去像是人在说“丝”-----“拉”

It rained on and off all night.(Indicating, the night is over and it has stopped raining) 雨咝咝啦啦下了一晚上

I studied Chinese on and off all day today (Indicating you have now stopped studying for the day with an emphasis on 'all day). 今天我断断续续学习了一天的汉语

你的“地”省略得都没有问题，而且所有的“de”都用对了。但是，我试了一下，这几个句子里“地”加与不加好像都一样。。。