Yo prefiero el rallador pequeño, pero mi hermana dice que el grande es más cómodo.

Yes, Spanish often drops them because the verb already shows the subject.

So Prefiero el rallador pequeño is perfectly correct.

Adding yo gives extra contrast or emphasis:

• Yo prefiero el rallador pequeño, pero mi hermana...
• It feels like I prefer the small one, but my sister disagrees

So yo is not required here, but it sounds natural because the sentence contrasts two opinions.

Because preferir is a stem-changing verb in the present tense.

The e in the stem changes to ie in most forms:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

So prefiero means I prefer.

El is the masculine singular definite article, meaning the.

Here it suggests a specific small grater, not just any small grater. The speaker is probably choosing between two known graters:

• el rallador pequeño = the small grater
• un rallador pequeño = a small grater

Also, rallador is a masculine noun, so the article is el, not la.

Because adjectives usually agree with the noun they describe.

The noun here is rallador, which is masculine singular, so the adjectives are also masculine singular:

• el rallador pequeño
• el grande
• más cómodo

Even in el grande, the noun rallador is understood, so the adjective still matches it.

In Spanish, descriptive adjectives usually come after the noun.

So:

• rallador pequeño = small grater
• coche rojo = red car
• casa grande = big house

Putting the adjective before the noun is sometimes possible, but it often changes the tone or adds a more subjective or literary feeling. In this sentence, the normal order is rallador pequeño.

Because Spanish often leaves out a noun when it is already obvious from context.

So:

• el grande literally means the big one
• The full idea is el rallador grande

This is very common in Spanish:

• Quiero el rojo = I want the red one
• Prefiero la pequeña = I prefer the small one

It avoids repeating the noun unnecessarily.

Gran is the shortened form of grande, but it is only used before a singular noun:

• un gran libro
• una gran casa

Since the noun is omitted in el grande, you must use the full form grande.

Also, gran often means something closer to great or impressive, not just physically big. Here the meaning is simply the big one, so el grande is right.

After decir, Spanish normally uses que to introduce what someone says:

• Mi hermana dice que... = My sister says that...

In English, that is often optional:

• My sister says the big one is more comfortable
• My sister says that the big one is more comfortable

In Spanish, que is usually kept, so dice que is the normal structure.

Because ser is used here to describe a more general characteristic of the object.

• es más cómodo = it is more comfortable / more convenient / easier to use

With objects, cómodo often means comfortable, handy, convenient, easy to use.

Estar cómodo is more common for people or animals in a temporary state:

• Estoy cómodo en esta silla = I am comfortable in this chair

For a grater being generally easier or more comfortable to use, es más cómodo is the natural choice.

Because más cómodo is more specific.

• más cómodo = more comfortable, handier, easier to use
• mejor = better

If the sister says el grande es más cómodo, she is specifically talking about comfort or ease of use, not necessarily saying it is better in every possible way.

So:

• El grande es mejor = The big one is better
• El grande es más cómodo = The big one is more comfortable / easier to use

It takes the indicative here:

• mi hermana dice que el grande es más cómodo

That is because this is a normal reported statement.

After decir que, Spanish usually uses the indicative when simply reporting information or opinion. The subjunctive appears in other structures, especially when decir means to tell someone to do something:

• Mi hermana me dice que use el grande = My sister tells me to use the big one

But in your sentence, it is just she says that..., so the indicative is correct.