Yes it works while plugged in and charging. I use it with a projector as well for Halloween decorations. However, remember to plug it into a separate power source if the Bluetooth speaker you are using never powers off. If your Bluetooth speaker powers off after a set time then you can plug the transmitter into the USB port of the projector for charging.
So far I've only paired 2 items at one time, cause that's all I've needed, But if the Speakers are a matched unit, and the IPhone is separate from the Speakers, I'm sure it'll work, But you can leave a question for the manufacturer Too be Positive!
Going on a bit of a flyer here, but I *think* you can do this from what I've read in the docs, but I have not tried it. I'm totally unclear how out behaves if you once active device on one input, and the second then goes active while the first is still active a well. I'd hope a Tao rep would chime in with a definitive answer.
This device allows you to connect multiple devices at the same time. As long as the devices are within range, you should have no problems getting your two bluetooth speakers connected. I have the device connected to the headphone jack on my amplifier for my sound system and I can have two bluetooth headphones connected and playing simultaneously.