Buksan mo ang bibig mo para makainom ka ng gamot.

They do two different jobs.

• The first mo marks the doer of the command: Buksan mo = You open it
• The second mo shows possession: ang bibig mo = your mouth

So even though both words are mo, they are not redundant.

Buksan means open in a form used when the thing being opened is the grammatical focus.

So:

• Buksan mo ang bibig mo = Open your mouth
• Literally, this structure is something like Open you the mouth your

It sounds strange in English if translated word for word, but it is normal Filipino grammar.

This is about verb focus.

• Buksan is an object-focus form. The thing being opened is marked with ang.
• Magbukas is an actor-focus form. The doer is more central, and the thing acted on is usually marked with ng.

Compare:

• Buksan mo ang pinto = Open the door
• Magbukas ka ng pinto = Open a door

In your sentence, ang bibig mo is the thing being opened, so buksan fits well.

Because ang bibig mo is the focused noun in the first clause.

With buksan, the thing affected by the action takes ang:

• Buksan mo ang bibig mo

If you used an actor-focus verb instead, the marking would normally change. So the choice of ang is tied to the verb form buksan.

Sometimes, but not always.

• The first mo in Buksan mo is important because it shows who should do the action.
• The second mo in ang bibig mo can sometimes be omitted if context already makes it obvious whose mouth is meant.

So:

• Buksan mo ang bibig mo = fully explicit
• Buksan mo ang bibig = possible in context, but less specific

In everyday speech, people often keep both.

Para means so that or in order to.

It introduces the purpose of the first action:

• Buksan mo ang bibig mo = open your mouth
• para makainom ka ng gamot = so that you can drink medicine

So the whole sentence shows a goal: open your mouth in order to take the medicine.

Makainom comes from inom (drink) and uses the prefix maka-.

Very roughly:

• uminom = to drink
• makainom = to be able to drink, to get to drink, or to manage to drink

In this sentence, makainom suggests that opening the mouth makes it possible for the person to drink the medicine.

So:

• para uminom ka ng gamot = so that you drink/take medicine
• para makainom ka ng gamot = so that you can drink/take medicine

The version with makainom adds a sense of ability or successful completion.

Because the two verbs use different grammatical patterns.

• buksan is object-focus, so the doer is marked by mo
• makainom is actor-focus, so the doer is marked by ka

That is why the same person, you, appears as:

• mo after buksan
• ka after makainom

This is a very common feature of Filipino grammar.

Because in makainom ka ng gamot, gamot is the non-focused object of the verb.

With actor-focus verbs like uminom or makainom, what is being drunk is usually marked with ng:

• Uminom ka ng tubig
• Makainom ka ng gamot

So ng gamot is the normal pattern here.

Yes. In Filipino, it is very common to say drink medicine where English would often say take medicine.

So:

• uminom ng gamot
• makainom ng gamot

can mean take medicine, especially if it is something swallowed by mouth.

If it is specifically liquid medicine, drink medicine is also a very natural literal translation.

It is understandable and natural enough, but many speakers would also say ibuka mo ang bibig mo.

A useful nuance is:

• buksan = open, in a more general sense
• ibuka = open wide / spread open, often used for the mouth

So both can work, but ibuka mo ang bibig mo may sound even more specifically like open your mouth.

A simple breakdown is:

• Buksan = open
• mo = you
• ang bibig mo = your mouth
• para = so that
• makainom ka = you can drink
• ng gamot = medicine

So the pattern is roughly:

• Verb + pronoun + ang-phrase + para + verb + pronoun + ng-phrase

This is very normal in Filipino. The sentence order does not match English word-for-word, so it is better to learn it as a Filipino pattern rather than trying to translate each part mechanically.