Pongo agua en la olla grande para cocinar pasta.

Yes, poner is fine and widely understood: Pongo agua en la olla…. Common alternatives, with slight nuances:

• Echar: very common for pouring/adding casually: Echo agua en la olla.
• Agregar / Añadir: “to add” (a bit more formal or recipe-like): Agrego agua a la olla.
• Llenar: “to fill”: Lleno la olla de agua. (focus on filling it up)
• Meter: “to put in” (more physical insertion): Meto agua en la olla sounds odd; use it for solid items: Meto la pasta en la olla.
• Verter: “to pour” (formal/technical): Vierto agua en la olla.

Pongo is the irregular first-person present of poner (“to put/place”). The yo form adds a g: pongo. There is no form “pondo.”

• Present progressive is also possible if you want “I’m putting”: Estoy poniendo agua…
• Some other key forms: puse (I put, preterite), pondré (I will put), pondría (I would put).

No article is needed because you’re talking about an unspecified amount of a mass noun (water): Pongo agua… = “I put (some) water…”

• Use the article when the water is specific or generic-in-general statements:
  • Specific: Pongo el agua en la olla (the particular water you mentioned).
  • General truths: El agua hierve a 100 °C.

Agua is feminine. It uses the article el in the singular to avoid the awkward sound of two a’s: el agua fría. Agreement stays feminine:

• Adjectives/pronouns: el agua fría, esta agua, mucha agua, la pongo en la olla.
• Plural: las aguas frías.
• With an intervening adjective, you can use la: la fría agua (literary).

With poner, the usual pattern is “put something in/on something” = poner X en Y.

• En la olla = in the pot (location/placement).
• A la olla can appear with other verbs (e.g., echar agua a la olla) where a marks the destination/indirect target. With poner, stick to en.

Yes, dentro de la olla emphasizes “inside” and is a bit more explicit:

• Pongo agua en la olla (standard).
• Pongo agua dentro de la olla (adds “inside”). Both are correct.

Yes. If the doer of the second action is different:

• Same subject: Pongo agua… para cocinar pasta.
• Different subject: Pongo agua… para que tú cocines pasta. (subjunctive after para que)

All can be used, with nuance:

• Cocinar pasta: general “cook pasta.”
• Hervir: “to boil.” You boil the water: Pongo el agua a hervir; then hiervo la pasta (many say “cocinar la pasta” too).
• Cocer: “to cook (often by boiling).” Many speakers say cocer la pasta. Note the irregular: cuezo, cueces. In much of Latin America, cocer and coser sound the same; context disambiguates.

No article is needed if you mean pasta in general/unspecified: cocinar pasta. Use the article when specific:

• General: Voy a cocinar pasta.
• Specific: Voy a cocinar la pasta (the pasta we already mentioned or have on the counter).

Yes, for a specific pasta already mentioned:

• Pongo agua… para cocinarla. (la = la pasta)
• Without a prior specific reference, keep it generic: para cocinar pasta (no pronoun).

Use the feminine direct object pronoun la (because agua is feminine):

• Specific water: ¿El agua? Sí, la pongo en la olla.
• Note: when agua is indefinite/mass (no article), you usually wouldn’t replace it with a pronoun unless you’ve specified it.

You have flexibility as long as it’s clear:

• Pongo agua en la olla grande para cocinar pasta. (natural)
• Pongo agua para cocinar pasta en la olla grande. (also fine)
• Para cocinar pasta, pongo agua en la olla grande. (emphasizes purpose) Keep related chunks together to avoid confusion.

Yes:

• Pongo el agua a hervir.
• Pongo a hervir el agua. Both are common and sound very natural when your goal is specifically to boil the water.

Yes, depending on the country:

• Olla (general “pot” everywhere).
• Cacerola / cazuela (saucepan/casserole-type pot).
• Paila (Andean regions; a wide, shallow pan/pot).
• Olla exprés / olla a presión (pressure cooker).