"比如说" is more common than the others you said, especially in speaking Chinese.

"玩腻了"means that you lost your interesting in doing that thing, and you don't want to do it anymore.For instance, you play a game many times and you don't want to play this game now, at the same time your friends ask you to play the game with them, then you can say "玩腻了".In Mandarin, a model case of double negative sentence is "不得不"。"不得不"means "have to". It always decorate with an action.For example, "不得不"do something and it means "have to do something". So, you can turn “玩腻了，我又到祖父那里去闹了一下。”into Chinese double negative sentence like this:“玩腻了，我不得不又到祖父那里去闹了一下。”I hope I can help you.

Thanks a lot Karen.

Good question. And I am in trouble in solve this question even my mother language is Mandarin.I try to differentiate the small difference between the two words and hope can help you. "以后" is more emphasis on the "time". "然后" is more emphasis on one thing is after another thing or one action is after another action.In addition, there is a pause when you say "我吃完了以后(pause)要去朋友家". "以后" has two meanings in Mandarin.The first is something has happend; The second is hereafter. In the sentence "我吃完了以后(pause)要去朋友家","以后" is the first meaning, and the pause is here. In the sentence "回家了(pause)以后你打算做什么?","以后" is the second meaning and the pause is here. Can you see the difference? "我先吃饭(pause)然后去朋友家","然后" is always close to the second action.

"遗失" is common in writing Mandarin. "I lost my book" means "我弄丢了我的书" or "我丢了我的书"。“我的书不见了”or " 我的书丢了” are both free translation. because "lost" in the sentence is a verb. in addition, you translate it into "我遗失了我的书". It sounds more influent. "了" in Mandarin always means something has occurred.I wish I can help you.

we use this grammer structure "越...越..." to express the meaning of you said.and just as "the more _(adj) the _(adj)_",we also use adj behind the word "越". I wish I can help you.