Learn French: Le doctorant sera prêt d'ici ce soir. - The doctoral student will be ready by tonight.

The à is generally optional when followed by a time expression. However, it is almost always dropped before demonstrative adjectives like ce (as in ce soir) or before common time words like demain. Saying d'ici ce soir is the most natural and common way to phrase this.

Does 'd'ici ce soir' mean he will be ready exactly this evening, or before then?

It means he will be ready at some point between now and this evening. D'ici literally means 'from here', so d'ici ce soir establishes a window of time starting from the present moment up to tonight. It is the perfect equivalent of the English 'by tonight'.

Could I use 'avant ce soir' instead of 'd'ici ce soir'?

You could, but there is a slight difference in nuance. Avant ce soir simply means 'before tonight', whereas d'ici ce soir emphasizes the duration of time starting from right now until the deadline. When you want to say 'by [time]' to express a deadline, d'ici is the most idiomatic choice.

How would this sentence change if the student were female?

You would need to make both the noun and the adjective feminine: La doctorante sera prête d'ici ce soir. Adding the -e to these words means you must now pronounce the final 't' sound in both doctorante and prête.