मेरी बहन मुझसे ज़्यादा जल्दी हिंदी सीख सकती है।

Because बहन is a feminine noun. In Hindi, possessives like मेरा / मेरी / मेरे agree with the noun they describe.

• मेरा = masculine singular
• मेरी = feminine singular
• मेरे = masculine plural or some oblique contexts

So:

• मेरी बहन = my sister
• but मेरा भाई = my brother

मुझसे is made from:

• मुझ = the oblique form of मैं (I / me)
• से = a postposition that can mean from, with, by, and in comparisons, than

So in this sentence, मुझसे means than me.

A very common Hindi comparison pattern is:

X + Y से + ज़्यादा ...
= X ... more than Y

So मेरी बहन मुझसे... means my sister ... than me.

Because Hindi pronouns often change form before postpositions like से, को, में, etc. This is called the oblique form.

For मैं, the oblique form is मुझ.

So:

• मैं = I
• मुझसे = from me / than me / with me, depending on context

Other examples:

• मुझे = to me
• मुझमें = in me
• मुझसे = from me / than me

So मैंसे is not correct standard Hindi.

Hindi usually does not use a special -er form like English faster. Instead, it often uses this structure:

Y से ज़्यादा + adjective/adverb

Here:

• मुझसे = than me
• ज़्यादा = more
• जल्दी = quickly / early / soon, depending on context

So मुझसे ज़्यादा जल्दी literally means more quickly than me, which is naturally translated as faster than me or sooner than me.

In Hindi, जल्दी can mean different but related things depending on context:

• quickly / fast
• soon
• early

In this sentence, because it is talking about learning Hindi, जल्दी means more quickly or faster.

So ज़्यादा जल्दी हिंदी सीख सकती है means can learn Hindi more quickly.

Because ज़्यादा is modifying जल्दी, so it normally comes before it.

This is like English more quickly, not quickly more.

Compare:

• ज़्यादा अच्छा = better / more good
• ज़्यादा तेज़ = faster
• ज़्यादा जल्दी = more quickly / sooner

So ज़्यादा जल्दी is the natural order.

This is a very common Hindi verb pattern.

• सीख comes from सीखना = to learn
• सकती comes from सकना = to be able to / can
• है is the present-tense auxiliary

So:

• सीख सकती है = can learn

The important thing is that after सकना, Hindi usually uses the verb stem, not the -ना infinitive.

So:

• correct: सीख सकती है
• not: सीखना सकती है

Because सकना agrees with the subject here, and the subject बहन is feminine singular.

So:

• वह सीख सकता है = he can learn
• वह सीख सकती है = she can learn

Since मेरी बहन is feminine, सकती is the correct form.

Because हिंदी is the direct object of सीखना, and in Hindi, non-human direct objects often appear without को.

So:

• हिंदी सीखना = to learn Hindi
• अंग्रेज़ी सीखना = to learn English

Using को here would sound unnatural in normal Hindi.

Hindi word order is fairly flexible, but the verb usually stays near the end. The given sentence is a natural, standard order:

मेरी बहन | मुझसे | ज़्यादा जल्दी | हिंदी | सीख सकती है

That is roughly:

my sister | than me | more quickly | Hindi | can learn

You may also hear variations for emphasis, such as moving हिंदी earlier, but the sentence as given is perfectly natural and easy to understand.

Yes, both ज़्यादा and ज्यादा are commonly seen.

• ज़्यादा reflects a pronunciation with a z sound
• ज्यादा is also very common in everyday writing

For most learners, it is best to recognize them as the same word, meaning more or too much, depending on context.

In this sentence, it simply means more.