I'm actually doing some research on MIFARE Classic 1K cards but there is an information that I can't find.
What is the ATQA size on a MIFARE Classic 1K card? I found some document that indicates it's 1 byte and some others 2 bytes.
I dumped a card and it seems like it is 1 byte, but ISO/IEC 14443-3 (6.4.2.1 - Coding of ATQA) indicates 16 bits.
The ATQA consists of 16 bits (2 bytes). It's defined by the ISO/IEC 14443-3 Type A anti-collision protocol (exactly what you found already). Thus, it has the same length for all cards/tags that implement that protocol (any Type A card/tag).
There is a different value also sent by the card during anti-collision (actually at the end of the anti-collision and selection procedure for a cascade level): the SAK (select acknowledge) which is a single byte.