imouto ha asagohan ni hamu to tamago wo taberuno ga suki desu.

The main predicate is 好きです, not 食べる.

A helpful way to chunk the sentence is:

妹は
→ as for my younger sister

[朝ご飯にハムと卵を食べるの]が
→ eating ham and eggs for breakfast

好きです
→ is liked / she likes it

So 食べる is inside a bigger phrase, and 好きです is what the sentence is really saying about that phrase.

は marks the topic of the sentence: as for my younger sister...

This is very natural when you are simply making a statement about her.

• 妹は～好きです = As for my younger sister, she likes...
• 妹が～好きです = It is my younger sister who likes... / My younger sister is the one who likes...

So が would sound more like you are identifying who likes it, while は just sets 妹 as the topic.

Usually, yes.

In Japanese, family words like 妹, 兄, 母, and so on often appear without words like my when the meaning is obvious from context.

So:

• 妹 = younger sister
• in many contexts, it naturally means my younger sister

If you wanted to make it explicit, you could say 私の妹.

Here, 朝ご飯に means something like for breakfast.

In this kind of sentence, Xに Yを食べる can mean eat Y for X, especially with meals:

• 朝ご飯にパンを食べる = eat bread for breakfast
• 昼ご飯にカレーを食べる = eat curry for lunch

So this に is not a destination marker here. It marks the occasion or slot: at / for breakfast.

と is the normal word for and when you are listing items together.

So:

• ハムと卵 = ham and eggs

This is a straightforward, complete list. If you were giving a non-exhaustive list, Japanese often uses や instead.

For example:

• ハムや卵 = things like ham and eggs

But in your sentence, と is the natural choice.

Because 食べる is modifying の, and before の you normally use the plain form.

So:

• 食べるのが好きです = likes eating
• not normally 食べますのが好きです

The politeness of the whole sentence is shown by です at the end.
This is very common in Japanese: a sentence can contain plain-form verbs inside it, while still ending politely.

Here, の turns the verb phrase into a noun-like idea.

So:

• 食べる = to eat
• 食べるの = eating / the act of eating

That lets the whole phrase function as the thing that is liked:

• ハムと卵を食べるの = eating ham and eggs
• ハムと卵を食べるのが好きです = likes eating ham and eggs

This use of の is called nominalization.

Because 好き does not behave like an English verb to like.

In Japanese, 好き is an adjective-like word, and the thing that is liked is usually marked with が:

• 犬が好きです = I like dogs
• 音楽が好きです = I like music
• 食べるのが好きです = I like eating

So が好き is the standard pattern.

No. 好き is usually treated as a na-adjective or adjective-like noun.

That is why it works with です:

• 好きです
• 好きじゃないです
• 好きではありません

A very literal way to think of it is closer to is liked / is pleasing than to the English verb like. That helps explain why Japanese uses が with it.

Yes, you could.

Both の and こと can nominalize a verb:

• 食べるのが好きです
• 食べることが好きです

Both are grammatical, but there is a slight nuance:

• の often sounds more direct, natural, and tied to a concrete action
• こと can sound a little more general or formal

For everyday actions like this, 食べるのが好きです sounds very natural.

Because the sentence is talking about liking an activity, not about wanting to do it right now.

Compare:

• ハムと卵を食べるのが好きです
  = likes eating ham and eggs

• ハムと卵を食べたいです
  = wants to eat ham and eggs

So 食べるのが好き describes a preference or habit, while 食べたい describes a current desire.