这里只能用 “二”，不能用 “两”。

两 and 二 are two different ways to say 'two' 两 is used when the quantity of the items are concerned. For example, 两个人 ， 两杯水。 第 can be used to turn the cardinal number into the ordinal number. For example, 一 means one, 第一 means 'the first' 二 means two, 第二 means 'the second' So, 第二 is correct but 第两 is not.

俩 两 仨，these words only used as number, don't use them with 第

第二次is correct , 第两次is not a good Chinese. Because 两 is used when you say "两个人，两双鞋，两只狗" something like that to indicate the number of objects or people.