HK, it's a mixture of both, really. Both of our parrots repeat what they've been taught or have just learned on their own, but they also make up their own sentences, sometimes quite nonsensical but funny. My Quaker is exceptionally intelligent and can use what words & sentences she knows in the right context for every situation.
You can read more about my Quaker in the thread "why do people say 'bird brain?' Birds are smart!"
My Buzzy tries to talk, but so far, he just babbles. I think he's trying to say "stretchy birdie," because whenever he stretches his legs and his wings, I say "Streeeetchy birdie!!" (I said it a few times when I first got him, and now he gets upset if he stretches and I don't say it). Every now and then he almost says something, but it turns into a squeak in mid-word. He can do sound effects, though! He can beep like the smoke detector and do a ringing phone sound.
jenb, when we had a cockatiel many years ago, that bird loved making the noise a microwave makes. He also loved whistling various tunes. It was funny when he'd pick up the specific whistled tune on a commercial. I think it was Lysol that might have had a whistled tune a long time ago, and he really loved that tune! He also would mimic a squeaky cupboard. Our Eclectus also likes making the squeaky cupboard noise! Birds are so amusing!
I wish we did have videos of a lot of funny stuff all of our animals have done. But, no, there's no videos at all of our cockatiel. He liked doing those "beep beep beep" noises the microwave does when the food is done. He could mimic them perfectly.
There was one time that a spider plopped down onto his head. I thought he'd shake it off immediately, maybe eat it or something, maybe freak out even. But he just sat there with this spider on his head, like a hat! As much as I'm terrified of spiders it was still hilarious. I can't remember what ended up happening. I'm sure I didn't get anywhere near that spider though! He probably did shake it off eventually and maybe it fell on the floor and I put a glass over it until the hubby could get home to kill it. I wish I'd had a video of him wearing that icky spider! haha
I have 2 Africian Red belly parrots. Both talk. Kito who is 8 is considered a service animal for me. Every morning when I uncover their cages both will say "good morning" to me, Then Kito will say "take you meds" a reminder to me to take meds. Until I give her a treat and say "thank you" she will continue to tell me to take my meds. Merlin has yet to tell me. Both birds will say "Tasha come here" or Kity, Kity Kity. Both dog and cat will come running up to their cages. Both parrots laugh, seems they can do that at just the right moment. Merlin likes to say "give me the remote" Kito will say "change the channel" both will make sounds like my cell phone, I have tried changing the ring tone but they seem to pic up it quick. Merlin has the foul mouth, I just don't know where he picked that up!
Tasha, your birds are so funny!!! I had to look up what an African Red Belly is - never heard of them. Very cute. Then I got stuck watching all kinds of parrot talking videos! :-)
Our birds will call our cats too "here kitty, kitty", but they will only actually name the Bengal cat if they see her. The Eclectus will sometimes still call our 2 dead cats, but neither bird acknowledges the current DSH and Tonkinese cats we have. They both hate the Tonk.
I love when the parrots laugh! Mine have never said bad words (thankfully!), though they've heard them too often! They must be very "good" birds!!! LOL
My Quaker still says, "Thanks for coming in. Come back soon," when we leave her room. She picked this up at the art gallery where we kept her the first several years of her life. She'd say that to the customers. For a long while she'd say my gallery's name whenever the phone rang here at the house (we moved her home when the business closed).