Yes,but you don't have a dedicated soundcard,it's an onboard sound chip.
Dedicated sound cards fit in the pci slots on your mobo and have all necessary connections.
Like i said it appears your onboard sound has all the necessary connections for 5.1 speakers.
Yep, most PC speakers use the green/orange/black colored jacks [3.5mm], and if you have RCA speakers [Red/White], you can buy a cheap RCA->3.5mm cable to make the connection. There are even 6.3mm (1/4") to 3.5mm cables out there for higher quality studio speakers.
If its analog, you can probably find a way to hook up the speakers you want to use.
It's mostly about what power & configuration your speakers need. If you don't have a sound card & are only using onboard sound (what you've pictured) Your speakers will always connect through here (bar a few exceptions like usb headphones),
There is 2 channels per port or plug and each channel has 2 wires/contacts.
If your speakers are 2 channel (left & right) theyll plug in the green one.
If your speakers are 5.1 channel as above (left, right, center, sub, rear left, rear right) theyll plug into green, orange, black ones