Learn Portuguese (Portugal): Respira fundo e começa o treino!

To give an affirmative command to someone you address as tu, you drop the 's' from the normal present tense tu form. For regular '-ar' verbs like respirar and começar, the tu forms are respiras and começas. Dropping the 's' gives us the commands respira and começa.

If the command form looks identical to the present tense form for ele/ela, how do I know it means 'Breathe!' and not 'He breathes'?

Context and tone of voice make it clear in real life. In writing, an exclamation mark is a big clue. Also, dropping the subject pronoun and starting the sentence directly with the verb is the standard way to give a command in Portuguese.

I learned that adjectives change to end in '-mente' to become adverbs. Why is it fundo instead of fundamente?

It is common in Portuguese to use certain adjectives in their basic masculine singular form as adverbs. Respirar fundo is a set phrase meaning 'to breathe deeply' or 'to take a deep breath'. Using the adjective fundo here sounds much more natural than adding '-mente'.

Does treino only mean 'workout'?