मेरी बहन के बाल लंबे हैं।

Because मेरी agrees with बहन, and बहन is feminine singular.

In Hindi, possessive words like मेरा / मेरी / मेरे change to match the noun that comes after them:

• मेरा भाई = my brother
• मेरी बहन = my sister
• मेरे दोस्त = my friends

So in मेरी बहन, the word मेरी matches बहन.

The phrase बहन के बाल means the sister’s hair.

Hindi often shows possession with का / के / की. These words do not agree with the owner; they agree with the thing being possessed.

Here, the possessed thing is बाल (hair / hairs), which is masculine plural, so Hindi uses के:

• बहन का कमरा = sister’s room
• बहन की किताब = sister’s book
• बहन के बाल = sister’s hair

So के is used because बाल is masculine plural.

In Hindi, when talking about someone’s hair in general, बाल is very commonly treated as a plural noun, literally hairs.

So:

• उसके बाल लंबे हैं। = His/Her hair is long.
• मेरे बाल काले हैं। = My hair is black.

This is normal and natural in Hindi. Even though English often uses singular hair, Hindi usually uses plural बाल for hair as a whole.

Because लंबे agrees with बाल, which is masculine plural.

The adjective लंबा changes form depending on the noun:

• लंबा = masculine singular
• लंबी = feminine singular
• लंबे = masculine plural

Since बाल is masculine plural, the correct form is लंबे.

So:

• बाल लंबे हैं = the hair is long
• किताब लंबी है = the book is long
• पेड़ लंबा है = the tree is tall/long

Because the subject being described is बाल, and बाल is plural.

Hindi uses:

• है for singular
• हैं for plural (and also as a polite form)

So:

• बाल लंबे हैं। = The hair is long.
• बाल लंबा है। would sound wrong in this context, because बाल is being treated as plural.

The main subject is बाल.

The phrase मेरी बहन के just tells you whose hair it is. The thing being described as long is बाल.

So the structure is basically:

• मेरी बहन के बाल = my sister’s hair
• लंबे हैं = are long

That is why लंबे and हैं both agree with बाल, not with बहन.

Not exactly. A very literal breakdown would be something like:

• मेरी = my
• बहन = sister
• के = of / ’s
• बाल = hair
• लंबे = long
• हैं = are

So the sentence is structurally close to:

My sister’s hair are long

That sounds odd in English because English treats hair differently, but it helps show the Hindi grammar.

Natural English would usually be:

My sister has long hair
or
My sister’s hair is long

Not in this sentence.

You choose का / के / की based on the possessed noun, and here that noun is बाल.

Since बाल is masculine plural, you need के.

Compare:

• मेरी बहन का कमरा = my sister’s room
• मेरी बहन की किताब = my sister’s book
• मेरी बहन के बाल = my sister’s hair

So की would be wrong here.

Some Hindi nouns do visibly change before postpositions, and some do not.

बहन is one of the nouns that usually looks the same in both its direct and oblique singular forms, so you still see बहन before के.

Compare that with a noun that does change:

• लड़का = boy
• लड़के का घर = the boy’s house

But:

• बहन की किताब = the sister’s book

So बहन is not staying the same by accident; that is just how this noun behaves.

Yes. लंबे and लम्बे are just spelling variants of the same word.

Likewise:

• लंबा / लम्बा
• लंबी / लम्बी

Both are understood, though लंबा is very common in modern standard writing.

मेरी बहन के बाल लंबे हैं। is already a very natural way to say it.

Hindi often expresses this idea as someone’s hair is long, rather than using a verb like has the way English does.

So even if the English meaning is My sister has long hair, the Hindi sentence मेरी बहन के बाल लंबे हैं। is completely normal and idiomatic.