Yes, it will fit into your motherboard provided it has a PCI-E x16 slot.
Iirc, the 710 does not require a power connector, but if I'm wrong, your PSU will have all required cables included (The Gigabyte has a very low power consumption so good choice)
Is it ATX, MATX or ITX? Whats the model name? Either way, it's a pretty small card so I doubt you would find problems trying to fit this card into any case