Assuming I attack with creature A, opponent assign creature B to block A, I exile it with Crib Swap, creating a changling. Can my opponent then assign that changeling to block me?
In general, creatures have only one opportunity to block during a combat phase, namely as the declare blockers step starts (C.R. 509.1). In general, a creature that enters the battlefield after blockers are declared in that phase, such as a token created with Crib Swap, can't be a blocking creature during that phase. Exceptions include if an effect specifically makes one creature block another, as in False Orders, or if an effect has the creature enter the battlefield blocking another creature, as in Aetherplasm or Flash Foliage (review C.R. 509.6, 509.7). See also this thread.
Assuming I attack with creature A, opponent assign creature B to block A, I exile it with Crib Swap, creating a changling. Can my opponent then assign that changeling to block me?
Shu Yun, the Silent Tempest WUR Voltron Control
Temmet, Vizier of Naktamun WU Unblockable Mirror Trickery
Ra's al Ghul (Sidar Kondo) and Face-Down Ninjas
Brudiclad, Token Engineer
Vaevictis (VV2) the Dire Lantern
Rona, Disciple of Gix
Tiana the Auror
Hallar
Ulrich the Politician
Zur the Rebel
Scorpion, Locust, Scarab, Egyptian Gods
O-Kagachi, Mathas, Mairsil
"Non-Tribal" Tribal Generals, Eggs
EDIT (Dec. 1, 2020): Correctness edit.
Shu Yun, the Silent Tempest WUR Voltron Control
Temmet, Vizier of Naktamun WU Unblockable Mirror Trickery
Ra's al Ghul (Sidar Kondo) and Face-Down Ninjas
Brudiclad, Token Engineer
Vaevictis (VV2) the Dire Lantern
Rona, Disciple of Gix
Tiana the Auror
Hallar
Ulrich the Politician
Zur the Rebel
Scorpion, Locust, Scarab, Egyptian Gods
O-Kagachi, Mathas, Mairsil
"Non-Tribal" Tribal Generals, Eggs