I know in Japanese there are multiple ways of saying ordinal numbers, each with their own nuances.
第〜, 〜目, etc.
There are also counters that don't need the ordinal marker like ページ, where 三ページ could be page 3 or three pages. My question is how do you ask which ordinal placement for each of these?
Do you use 何 like with most measure words, or do you use どの?
Most of your questions have already been answered in the past, so allow me to write an answer with many links.
3ページ ("page 3" or "3 pages) and 3ページ目 ("third page") are different. Please read this: Leaving away the 目 suffix for ordinal numbers
The difference between 第 and 目 is summarized in this question: 第 [dai-] vs 目 [-me] in forming ordinal numbers It's good to think of 第 primarily as a formal method to label sequential things (artworks, book sections, events, shops, etc) in numerical order. Unless you are writing a book in Japanese or hosting an event in Japan, it is rare to name something with 第 in daily life, so you should first get used to using 目.
English lacks a way of asking "how manieth", but in Japanese, you can construct such question easily using "何 + counter + 目". See: How do you ask for ordinality (order in a sequence)?
