Can an iPhone connect to two WiFi networks at once? For instance home WiFi and airplay speaker at the same time.

The link I provided should give you information about connecting your devices together using AirPlay. I know you should be looking at the AirPlay area when attempting to play music, not your wi-fi settings. When I wish to use AirPlay, I go to the Music, and tap on the AirPlay icon and I can see my TV. That is the only device that I have that is AirPlay compatible. What happens when you tap on the AirPlay icon? Do you see the speaker? Is the speaker advertised as AirPlay compatible, or is it supposed to connect via Bluetooth?

One at a time. Why isn't the AirPlay speaker on the same network? According to this, If AirPlay or screen mirroring isn’t working on your device - Apple Support they need to be on the same wi-fi network.

Thats not really connecting to 2 wifi's at the same time but yes, you can be on your home wifi and connect to your airplay device at the same time (assuming your airplay speaker is on the same network)