Q1. Why is the article's name "Czech Republic" and not "Czechia"?
The "Czech Republic" is the official name of the country and the term is so far more widely used and recognized in English than "Czechia". The name of the Wikipedia article is attributed to a broad consensus on this page (Talk:Czech Republic/Archive 7#Requested move 19 June 2018), which was unchanged after a subsequent discussion at Talk:Czech Republic/Archive 8#Requested move 22 November 2019 and Talk:Czech_Republic/Archive_10#Requested_move_25_July_2021. This question may be revisited in the future.
Q2. Is this the correct place to discuss whether to use "Czech Republic" vs. "Czechia" in other Wikipedia articles?
No, this talk page is only for discussing improvements to the article "Czech Republic", the same goes for other article talk pages.