How to use -ㄹ래야 and -려니?
I'm preparing for TOPIK and I would like some examples and explanations from native/fluent speakers. How do I use -ㄹ래야 (with verbs) and -려니 and what do they mean?

Also, is there any difference between these three grammar patterns:
1. ㄹ 만큼
2. ㄹ 정도로
3. ㄹ 지경이다

I understand they all mean basically the same thing, "(it's) so that I almost ", but are there any differences between them? Like are some of them used only in certain situations or something else?

Question

How to use -ㄹ래야 and -려니?
I'm preparing for TOPIK and I would like some examples and explanations from native/fluent speakers. How do I use -ㄹ래야 (with verbs) and -려니 and what do they mean?

Also, is there any difference between these three grammar patterns:
1. ㄹ 만큼
2. ㄹ 정도로
3. ㄹ 지경이다

I understand they all mean basically the same thing, "(it's) so  that I almost ", but are there any differences between them? Like are some of them used only in certain situations or something else?

Answer

'-ㄹ래야' is a wrong expression of '-래야'. 
'-래야' is shorthand for '-라고 해야'. It shows that you talk about something with taking it all in stride. For example, "월급이래야 이 정도가 전부다." Also you can use it with a verb, when you decide to tell someone what to do. "그사람한테 전화해서 여기로 오래야 겠다." (I'd call him to come over here.) 
'-려니' shows that you conjecture about someone or a situation or something.
"그가 전화를 받지 않길래 자고 있으려니 하고 생각했다." (He didn't answer the phone, so I thought he was sleeping.)

There is not much in it with '-ㄹ 만큼' and '-ㄹ 정도로'. But '-ㄹ 지경이다' is used to say when you are on the edge of a situation and you feel like you can't stand any longer. "일이 너무 많아 쓰러질 지경이다."
Or you can use it in a situation that you just can't wait even one second to do something. "그를 빨리 보고 싶어 참을 수 없을 지경이다." :)