Yes they do, Canon Powershot SX510 HS is one of them. I also know they make attachments as well. Google canon image gateway and they will give you more information
Canon PowerShot ELPH 320 has built-in WIFI. There are a number of others that include this. You can also use en EYE-FI card with any of them which effectively provides a WIFI connection for any that support it although I found the EYE-FI setup to be a little convoluted.
I purchased a Sunpak DigiFlash 3000 for my camera and don't really know much about your Speedlite but if it fits onto the shoe on top of the camera it probably will work. Try it and see.