It's interesting to see how there is more than one solution. I completed most of these in another way:
Puzzle #1
1. Taldaram the abomination and attack immediately
2. Silence anything not important
3. Soulfire a giant (thus discarding the kidnapper)
4. Attack a giant with the dinomancer
5. Kill the last giant with the kidnapper that spawns from the dinomancer.
Puzzle #3 I vanished then just got lucky and stole the novice engineer and faceless manipulator.
Puzzle #4 I managed to find the most complicated solution possible to this one.
1. Use shadow madness on gilda
2. Taldaram the malg'ganis
3. Give the mal'ganis copy immune with deathspeaker
4. Kun to refresh mana
5. Use treachery on the immune copy
6. Attack with the abomination into the voidlord (which now has 5 attack from the mal'ganis buff)
7. Hero power the abomination to get some board space
8. Copy the aviana again
9. Copy the mal'ganis again
10. Kun to refresh mana
11. Give immune to the copy on your side with the deathspeaker
12. Attack with the original mal'ganis into the voidlord (thus killing both)
13. Play kun and refresh mana one last time
14. Ray of roasting. Now there are 3/3 mal'ganises with immune on both sides of the board.
6