whilst 텐데(요) and 테니까 have their own satisfactory grammar documentation, 테다 is missing its own exhaustive coverage.
I'll include the example sentence that made me curious in the first place:
죽여버릴 테다
Is there any nuance that 테다 contains over its counterparts, or is it simply expressing the same strong expectation/intention with emotion, but without making that subsequent suggestion or evaluation when 으니까 or ㄴ데 are used?
The form -ㄹ 테다 expresses expectation or intention. In practice, its most common usages are in the context of 텐데(요), 테면, and 테니(까). However, as you point out, it can be used more directly in the infinitive form of 테다 (although the other forms are more common in practice). Usually, when it is used in this way, it is the first person imperative.
안 줄 테야 (I will not give it to you)
난 꼭 하고야 말 테다 (I have something I must say!)
Keep in mind that 테다 is really just a shortened form of 터 이다, with 터 being a 의존 명사 (dependent noun). Very loosely speaking, we can think of 터 operating in a grammatically similar form as to 것 in Korean. Hence, anything that you could do with 것이다 would in theory work for 터 이다 (테다). When used in the infinitive form (터이다/테다), the most natural usage is in the first person.
