Se hai sete, bevi pure dalla bottiglia: l’acqua è freschissima.

Here pure is an adverb meaning “go ahead” or “feel free.” It’s not the same as the English word pure. In bevi pure it softens the command, turning it into a friendly invitation:

• Bevi pure! = “Go ahead and drink!”
  You see this same usage in phrases like vieni pure (“come on in”) or chiedi pure (“feel free to ask”).

Avere sete is an idiomatic expression: you don’t use an article with these “state of being” nouns. Compare:

• avere fame, avere freddo, avere caldo
  So you say hai sete (“you’re thirsty”) rather than hai la sete.

Bevi is the tu (second-person singular) form. In the imperative mood (affirmative), bere (to drink) is irregular:

• tu bevi (imperative)
• Lei beva (formal imperative)
• voi bevete
  If you used beve, that would be the third-person singular indicative (“he/she drinks”), not an instruction.

Freschissima is the absolute superlative of fresco (fresh). You form it by attaching -issim- plus the ending matching the gender/number:

• fresco → fresch- + ‑issimo → freschissimo (masc. sing.)
• fresca → fresch- + ‑issima → freschissima (fem. sing.)
  It means “extremely fresh” or “very, very fresh,” stronger than molto fresca.

The colon introduces an explanation or result of the first clause. You could also write:

• “Se hai sete, bevi pure dalla bottiglia, perché l’acqua è freschissima.”
  But the colon is a stylistic choice that tightens the link: “If you’re thirsty, do this: the water is extremely fresh.”

Se hai sete uses the present indicative for a real condition (“if you really are thirsty”). In Italian you don’t use the subjunctive in first (real) conditionals. The pattern is:

• Se + present indicative, then main clause (here an imperative).