Learn French: Je finirai ma thèse d'ici demain matin. - I will finish my thesis by tomorrow morning.

When the deadline is an adverb of time like demain, bientôt, or ce soir, you drop the à and just use d'ici. You typically only need d'ici à before a noun phrase with an article (like d'ici à la semaine prochaine) or a specific month or year.

Could I use jusqu'à instead of d'ici to mean 'by tomorrow morning'?

No, because jusqu'à means 'until' and describes an ongoing action. If you said Je travaillerai jusqu'à demain matin, it means you will work continuously until that time. D'ici means 'by' or 'between now and', showing that the single event of finishing will happen at some point before the deadline.

Is it wrong to use the future perfect (j'aurai fini) here?

Not at all! J'aurai fini ma thèse d'ici demain matin (I will have finished my thesis by tomorrow morning) is also perfectly correct and very common. The simple future (Je finirai) emphasizes the action of finishing itself, while the future perfect emphasizes the completed state of the thesis.

Does une thèse translate to any university 'thesis'?