Standard desktop hard drives are going to be 3.5” drives. The same is true for that SSHD you have. Replacing that drive is as simple as taking it out and screwing the new one in.
As for SSD’s, they are smaller at 2.5”. If your case does not have a slot for it then you can buy an adapter like this one -
http://www.newegg.com/Product/Product.aspx?Item=17-979-016 - and use it properly place an SSD in a 3.5” bay (should you have one available).
Moving to your second question, the only thing you need to check is that you have space for multiple drives and enough SATA ports. Most motherboards come with plenty of ports and yours should have at least two available. You also need to buy a SATA cable for your SSD if you don’t have one.