The article is plural because horas is understood: a las ocho, a las nueve y media. One o'clock is the only singular: a la una.

Ranges: de las nueve a la una, entre las tres y las cuatro.

The trap: your notes state the rule in exactly these words, because a las una is the mistake everybody makes once.

a las diez is a point on the clock. por la manana is a stretch of the day, used for repeated actions.

They combine, in that order: Me levanto a las diez por la manana.

With an exact hour you can also say de la manana or de la tarde: a las nueve de la manana.

The trap: never en la manana in this course, and never a la manana.

antes de cenar = before having dinner. despues de tomar cafe = after having coffee.

The sequencers that start a clause take a normal conjugated verb instead: primero desayuno, despues me ducho, luego me visto, entonces me lavo los dientes, al final salgo de casa.

The trap: despues on its own means afterwards and needs no de; despues de needs a verb or a noun after it. Both appear in the same class exercise.