Q1: Is مَرَرْتُ بِهِنْدٍ incorrect? No. The text permits both full and restricted declension for qualifying Hind.
Q2: Must حَمْرَاءُ be fully declinable because it is not a name? No. Feminine alif mamdūda is independently sufficient.
Q3: Why is مَدْرَسَةٍ genitive with kasra? It has a feminine tāʾ but does not meet the proper-name condition.