Is there any difference between beginning a sentence with 在北京游览 and （你）在北京游览（时候/时）?
在北京游览，乘坐什么交通工具比较方便。
(When) On tour in Beijing, the public transportation system is relatively convenient.

在北京游览，is a general reference, not aimed at any specific 你, so no 你 is mentioned.

Chinese is direct, "在吃饭，我用筷子。" is wordy. Try:

我用筷子吃饭。

You could try entering "Chinese grammar of zai" in any search engine, you will get a lot of results. I got 161 million results!