The defense seeks to introduce into evidence statements made by a third party suspect allegedly admitting to the offense.
The State objects to the statements because they are not substantially corroborated under Rule 803(24) (the declarant gets the facts all wrong) and the judge then excludes them.

Can the defense then come back and call the third party suspect to testify then impeach him with said statements as prior inconsistent statements, even though substantive evidence of them has already been excluded because it was not reliable?

Hughes v. State, 4 S.W.3d 1, 6-7 (Tex. Crim. App. 1999)(calling witness just to introduce impeachment evidence violated Rule 403)

What if the State calls the third party suspect itself? Does that then allow the defense to impeach him with the prior alleged statements that have been previously excluded due to their dubious reliability?

They might offer it as a prior inconsistent statement.

I would think that if you put the guy on the stand to say the defendant did it, you couldn't prevent the defense from asking him if he had previously said something different.