Learn Hardcore Portuguese (Portugal): Esse treino é curto, mas deixa-me cheio de energia. - That workout is short, but it leaves me full of energy.

Este treino would imply the training is close to the speaker or about to start now.
Aquele treino would refer to a training session farther away in time or space (e.g. a past or very distant event).
So you choose este, esse or aquele based on how close or familiar the training is to speaker/listener.

Why is the pronoun placed after the verb as deixa-me instead of before it as me deixa?

Portuguese has rules for clitic pronoun placement:

After a pause (comma) or at the very start of a clause, European Portuguese prefers enclisis (verb + pronoun): deixa-me.
Proclisis (pronoun + verb) like me deixa often appears when there’s a negative word, question word, or certain conjunctions requiring it.
Here, the comma before mas creates a “new clause,” so enclisis is the norm.

Could I say me deixa cheio de energia instead of deixa-me cheio de energia? Would it sound wrong?

You can say me deixa cheio de energia, and native speakers will understand you perfectly.

In European Portuguese, deixa-me is more formal/standard after punctuation.
Colloquially (and especially in Brazilian Portuguese), me deixa is very common.
Neither is “wrong,” but choose enclisis for a more European-Portuguese feel.

What does cheio de energia literally mean, and are there other ways to express it?

Cheio de energia literally means “full of energy.”
Alternatives include:

Repleto de energia (a bit more formal)
Com muita energia (with lots of energy)
Super energizado (informal, “super energized”)
They all convey that you feel very energetic after the training.

What part of speech is curto, and can it change form?

Curto is a masculine singular adjective meaning “short.”

Feminine form: curta (e.g. essa sessão é curta)
Plural forms: curtos (masc.) / curtas (fem.)
It agrees in gender and number with the noun it modifies.

Why don’t we use an article before treino, like o treino é curto?

You can say O treino é curto, mas… with a definite article; it simply feels more “introduced” or generic.
Using Esse treino already contains a demonstrative plus noun, so adding o would be redundant. If you wanted “a certain short training,” you could say Um treino é curto…, but that changes the meaning.

Is there anything special about using mas here instead of another conjunction?

Mas is the standard coordinating conjunction for “but” and contrasts two statements.

You could also use porém or no entanto for a more formal tone:
“Esse treino é curto; porém, deixa-me cheio de energia.”
But mas is the most common and natural in everyday speech.