Moaning: Cats may moan to seek attention, express hunger or thirst, signal pain or discomfort, or react to stress and anxiety.
Carrying things in mouth: Mother cats carry kittens to protect them. Cats may also carry prey due to hunting instincts, toys for play, or objects like blankets for comfort.
Observe your cat's behavior to understand the cause. If you are concerned, consult your veterinarian.