Unlike a spawn egg, chickens only have a 12.5% chance of coming out of an egg, as compared to 100% from a spawn egg. In any case, since there is already a Chicken Spawn Egg, this seems to be working as intended.
Sculk shriekers cannot spawn wardens when placed down by a player, as it's NBT tag of "can_summon" gets set to false. This is most likely working as intended. See MC-250137
Not a bug, but rather JSON structure...? Text will intend to inherit the previous formatting because there has been no new formatting specified. Using a blank string ( "", ) at the start implies that every string's formatting will need to be specified on their own, breaking this inheritance.
You can use /tellraw @s ["",{"text":"-1 ","color":"red"},{"text":"secondary test"}] to achieve your intended effect.
Sounds like a dupe of MC-277889?