Saying her own name: Admittedly, it sounds like she's saying 'Allah', which may well be grounds for a fatwa. To be fair, 'Olivia' is quite a difficult word to get right, and it does sound more like 'Aaalughuh'.
Reading her own name: On Olivia's bedroom door is a big, pink wooden butterfly with block capital letters spelling out her name. On the wall above her bed, are six canvasses about 20 cm square, each with a letter upon it. Whenever we go into her room, I make a point of tracing over the letters and spelling out her name on one or other. When we realised she was saying her name, I thought I'd see what happened if I pointed at her name and asked her what it said. 'Allah,' came the reply. I was somewhat gobsmacked. It hadn't really occured to me it might work, but we've written it on various bits of paper since and she definitely gets it right. without prompting beyond, 'What does that say?'
She can also tell you that the last letter is an 'A', but I'm not so sure that's genuine. Certainly with the recognising her own name, she's recognising it as a block of letters, rather than reading it. It's more akin to recognising a logo than proper reading, but nevertheless pretty good.
Swimming: We went to our local swimming pool last weekend, and I remarked to K___ how much more confident Olivia was in the water. We went again today, and bugger me with a Sherman Tank if she didn't 'swim'! She was in water that was up to my stomach, so way out of her depth, and she was lying on her front and kicking a few strokes totally unsupported. She also lay on her back and floated, again unsupported. In neither case did she do it for long, but it was five seconds or so. and all the while she was beaming like she was Esther Williams.
Obviously, she had armbands on and I was ready to grab her at the first sign of any trouble, but I was still really surprised.
Singing: Duetting, in fact.
Me: "Tinky Winky... Dipsy..."
Olivia: "Laaaa-Laaa... Po..."
Me: "Teletubbies... Teletubbies... Say 'Eh-oh'!"
As an aside, I bought a couple of episodes of Teletubbies from iTunes the other day, because Olivia's obsessed with it. We sat through one and I thought nothing of it. Later on, I logged onto LastFM only to discover one of my LastFM buddies questioning my sudden love for children's T V characters because it got picked up and reported onto the site. Now deleted.
Anyway, so while Baby 2 is apparently happy remaining in situ for a little longer, we've got plenty to occupy us with Baby 1.