Question

general.css

#feedback_bar
{
  /*props*/
}

another.css

#feedback_bar
{
  /*props*/
}

Is this allowed? Will both get inherited?

Answer 1

The properties defined last will override properties defined previously. Unless you use !important on the previously defined section of CSS.

.thing {
    padding: 10px;
}

.thing {
    padding: 12px;
}

.thing will have padding: 12px;

.thing {
    padding: 15px !important;
}

.thing {
    padding: 123px;
}

.thing will have padding: 15px;

This is allowed, and to more strictly answer your question, both will indeed be inherited as shown by this example:

.thing {
    padding: 10px;
}

.thing {
    background: red;
}

.thing will have both padding: 10px; and background: red;.

Also, please take a moment to read some of the comments on this answer as they raise good points worth further reading.