Learn Portuguese (Portugal): Eu fiz uma surpresa à minha mãe.

No, fiz is the highly irregular past tense (Pretérito Perfeito) of fazer (to do/make) for eu (I). Because it is irregular, its stem changes completely to fiz-, breaking the normal rules you learned for regular -er verbs.

The translation says 'for my mother'. Why does the sentence use à instead of para a?

In Portuguese, the phrase is fazer uma surpresa a (literally 'to make a surprise to'). The word à is a contraction of that preposition a (to) and the feminine article a (the).

Why is there an article 'the' hiding inside à right before minha mãe?

In European Portuguese, it is standard to put a definite article like o or a before a possessive word. You say a minha mãe (literally 'the my mother'). When the preposition a (to) meets the article a (the), they merge into à.

Can fiz also mean 'did' instead of 'made'?

Yes! The verb fazer covers both 'to make' and 'to do'. Depending on the context, eu fiz means 'I made' (like in this sentence) or 'I did' (like eu fiz o meu trabalho for 'I did my work').