Translation is always tricky, but I understand that some schools, especially American schools, believe that a Chinese course should include a translation element. Let's give it a go in the way that you suggested - analysing the sentences rather than giving you the complete translations. 1. She was at a meeting when I got to her office. The trick here is to state your arrival first, using "…的时候". You need a reversal of order of the two clauses when you write them in Chinese. 2. At first, I wrote very slowly. But later, my big brother helped me practice.  The trick here is to learn the "standard" expressions for "at first" and "but later". These are: "刚开始的时候" and "但后来". Now you are ready to do the translations yourself. Let us have a look. We shall help you correct them. ------ This seems to be an exercise in "的时候".

1. She was at a meeting when I got to her office. the clause that describes the time need to be put at first, then in chinese, it'll be like" when i got to her office, she was at a meeting." To translate "when", You can put "的时候”at the end of the clause. 2. At first, I wrote very slowly. But later, my big brother helped me practice. "at first" can be translated as "一开始“, you can use "但后来“ to express "but later", "但" means "but", ”后来“ means "later" Hope these can help you

1. we use 当 to show "at the same time/when", the sentence order would be——“ 当……，她……” in our mental lexcon, this scene is all around ourselves. we see the world with ourselves as a center. so the image in the mind is "I got to her office, I saw that she was at a meeting", so the order of our sentence is the same as the image in our mind. of course, if you want to express "she was at a meeting" particularly or as the main meaning, you can put it ahead of the sentence——“她正在……当我……”, it's not the most natural order to express such a meaning, but we can use it when we think it needs to. 2."at first……，but later……“ would be "刚开始……，但后来……“ this order has the same reason as the first one: it go with our memory, the way you thinking. the sentence A and B after 刚开始 and 但后来 can be two independent sentences separatly. that's all i know. wish to help. I'm not a linguist but a university student, but you can think about it.