I'll try to answer your question one by one.
1) What does "Vậy ra cái" mean in the following sentence?
→"Vậy ra cái" is not a word. You must break the sentence apart like this:
"Vậy ra | cái buổi sáng | mà tôi đã gặp cậu,..."
→So | the morning that | I met you...
2) What does "đó sao" mean in the following sentence?
-→"đó sao" is similar to tag question in English when you desire to be responded.
Cậu chẳng bao giờ trả lời các câu hỏi, thế nhưng, khi người ta đỏ mặt, thì đấy chẳng có nghĩa là "phải" đó sao?
→You never answer questions, but, when your face become red, it means "Yes", doesn''t it?
3) What does "kịp đón" mean in the following sentence?
Tôi tới chỗ bức tường cũng vừa kịp đón được trong tay chàng hoàng tử nhỏ bé, trắng bệch như tuyết.
→in this case "kịp đón" means to catch up in hands.
the little prince was falling down and "I" came to the wall to catch him.
