From what I'm reading about this rose, it tends to grow large for a miniature. Miniature roses don't require much pruning, just for shape. After a cane is finished flowering you should prune to a new outward facing bud. You can prune shoots that emerge from the soil or leave them to grow. If you find they are too spindly you can prune the entire plant by about one third. They might be reaching for the light and that could cause them to become spindly.
I suspect that your rose flowers were either finished blooming or possibly fell due to climate change when you brought the plant home. Overwatering, underwatering or being rootbound can cause this too. Look at the bottom drainage holes to see if you see roots there. If not, gently remove the plant from it's pot to see if it needs a new pot 2" larger.
I would suggest you remove the wrapping paper and use some type of saucer so you can better see if the plant is standing in water. Water when the top inch of soil is dry. You can insert your finger to the first knuckle. Don't let the soil dry completely.
As to the fertilizer you are using, it would depend on what is in it. Generally a well rounded 20-20-20 is good. Use at half strength. I prefer organic fertilizers such as fish emulsion or fish emulsion mixed with sea kelp. Careful when you open the bottle as the smell is quite strong. It will dissapate in the water.
You should find this helpful.