Can you build a house on a colour group property while another property of that colour group is mortgaged?
No you are unable to build houses on any property in a color group where any property is mortgaged. While it does not mention it in the rules about houses it does mention that all hotels and houses must be sold prior to mortgaging any property of that color group. The rules also follow up with an explicit statement that you may begin to buy houses back once all properties in that group are no longer mortgaged.
Rules

MORTGAGES… Unimproved properties can be mortgaged through
the Bank at any time. Before an improved property can be mortgaged,
all the buildings on all the properties of its color-group must be sold
back to the Bank at half price. The mortgage value is printed on each
Title Deed card


When all the properties of a
color-group are no longer mortgaged, the owner may begin to buy
back houses at full price.