मुझे यह सबक याद है।

Because Hindi usually expresses remembering with a different structure from English.

Instead of saying I remember this lesson, Hindi commonly says something closer to:

To me, this lesson is remembered.

So the person who has the memory appears in the dative-like form:

• मैं = I
• मुझे = to me / me

That is why मुझे यह सबक याद है is natural, while मैं यह सबक याद है would be incorrect.

मुझे is the form of मैं used for meanings like to me or me in certain constructions.

In this sentence, it marks the experiencer — the person to whom the memory is present.

You can think of it as:

• मुझे = to me
• मुझको = a fuller version with the same basic meaning

So:

• मुझे यह सबक याद है
• मुझको यह सबक याद है

Both are possible, though मुझे is very common and natural.

Because यह is the direct form of this, while इस is the oblique form used before a postposition.

Here, यह सबक is standing directly in the sentence, with no postposition after यह, so Hindi uses यह.

Compare:

• यह सबक = this lesson
• इस सबक में = in this lesson
• इस सबक को = this lesson (with को)

So in your sentence, यह is the correct form.

Not by itself. In मुझे यह सबक याद है, याद is part of the expression याद होना, which means to be remembered / to be in memory.

So the full idea is:

• याद है = is remembered / is in memory

This is different from याद करना, which means to memorize or sometimes to remember in a more active sense.

So:

• मुझे यह सबक याद है = I remember this lesson / I know this lesson by heart
• मैं यह सबक याद करता हूँ = I memorize this lesson / I am learning this lesson by heart

Because the sentence is not built around I am.

The grammatical center of the sentence is really यह सबक — this lesson — and Hindi is saying that this lesson is remembered.

So the singular copula है is used.

A helpful way to see it:

• मुझे = to me
• यह सबक = this lesson
• याद है = is remembered

If the remembered thing were plural, you would usually use हैं:

• मुझे ये सबक याद हैं। = I remember these lessons.

So है / हैं depends on the thing remembered, not on मुझे.

A very literal breakdown is:

• मुझे = to me
• यह = this
• सबक = lesson
• याद = remembered / in memory
• है = is

So the sentence is roughly:

To me, this lesson is remembered.

That is why the natural English translation becomes I remember this lesson.

Yes, Hindi word order is somewhat flexible, though some orders are more neutral than others.

The most neutral order here is:

मुझे यह सबक याद है।

You may also hear:

• यह सबक मुझे याद है।

This can put a little more focus on this lesson.

Even when the order changes, the meaning usually stays the same because the roles are still clear from the forms and the overall pattern.

It can mean either, depending on context.

With सबक (lesson), it often suggests:

• I remember this lesson
• I know this lesson by heart
• I have this lesson memorized

So याद है covers both having something in memory and knowing it from memory.

Context tells you which English wording sounds best.

Add नहीं before है:

मुझे यह सबक याद नहीं है।

This means:

I do not remember this lesson.

In casual speech, people sometimes drop है, but for learners, the full standard form is best:

मुझे यह सबक याद नहीं है।

You can add क्या at the beginning:

क्या मुझे यह सबक याद है?

That means:

Do I remember this lesson?

In speech, intonation also helps show that it is a question.

You could also ask someone else by changing the pronoun:

• क्या तुम्हें यह सबक याद है? = Do you remember this lesson?
• क्या आपको यह सबक याद है? = Do you remember this lesson? (polite)

You can, but it does not mean exactly the same thing.

• मुझे यह सबक याद है = I remember this lesson / I know it by heart
• मैं यह सबक याद करता हूँ = I memorize this lesson / I commit this lesson to memory

So if you want to describe your current state of remembering, मुझे ... याद है is the normal choice.

If you want to describe the action of memorizing, then याद करना is the better form.