Yes, keep faded blooms cut off. This will encourage new growth and new blooms to form.
If the first blooms dried up before they opened it most likely was due to the conditions that the plant was growing in in the greenhouse. Now that it is adjusting to conditions in your garden it will have to adjust to new conditions of light and humidity.
Be sure that there is good bottom drainage and you might consider using an all-purpose rose fertilizer at half-strength.
Hope this is helpful.
Meg