Is it possible to define Tier's level of Subscriber (1, 2, 3) in Twitch Extension (by Twitch API)?

More or less. Be careful about assuming that sub_plan 1000, 2000, 3000 maps to $4.99, $9.99, and $24.99, that isn’t always the case.
You also shouldn’t assume anything about the sub_plan_name. There are other fields in the payload that more explicitly tell you what you’re looking for.