Portami quel nastro verde: voglio legare i fiori prima che appassiscano.

Portami is the affirmative imperative of portare (to bring) plus the indirect-object pronoun mi (to me). In Italian, when you give a positive command to tu, you attach object pronouns to the end of the verb:
• porta (bring!) + mi (to me) → portami (“bring me”).

Italian demonstratives agree in gender, number and take different forms depending on the initial letter of the noun:
• quel: masc. sing. before most consonants (e.g. quel nastro)
• quello: masc. sing. before s+consonant, z, ps, gn, x, y (e.g. quello studente)
• quella: fem. sing. before consonants (e.g. quella casa)
• quell’: sing. before any vowel (e.g. quell’uva)
Here nastro is masculine singular starting with n, so we use quel.

Most Italian color adjectives come after the noun, unlike English. Verde ends in -e in the singular, so it’s the same for masculine and feminine. Only in the plural does it change to verdi (for both genders):
• un nastro verde, una foglia verde
• due nastri verdi, due foglie verdi

• prima che + subjunctive is used when the subject changes and you’re talking about something before it happens: here the flowers (they) may or may not wither. So you need the subjunctive appassiscano.
• prima di + infinitive is only possible when the subject of both verbs is the same (e.g. “Finisco il lavoro prima di uscire”).

Yes. To avoid repeating i fiori, attach the direct-object pronoun li to the infinitive: drop the final -e of legare and add li → legarli. So you get:
voglio legarli prima che appassiscano
where li = “them” (the flowers).

No, it’s a stylistic choice to link purpose and request. You could use a comma or separate sentences:
• Portami quel nastro verde, voglio legare i fiori prima che appassiscano.
• Portami quel nastro verde. Voglio legare i fiori prima che appassiscano.