सदस्यता में फ़िटनेस क्लास है।

Literally, it is something like:

In the membership, there is a fitness class.

Hindi often uses the pattern X में Y है to say that Y is in / part of / included in X.

So:

• सदस्यता में = in the membership
• फ़िटनेस क्लास = fitness class
• है = is

That is why the Hindi word order feels different from the English The membership includes a fitness class.

Yes, में basically means in or inside, but here it is being used a little more broadly.

In this sentence, सदस्यता में means:

• in the membership
• as part of the membership
• included in the membership

So में is not always just physical location. It can also show that something belongs within a package, category, plan, list, etc.

For example:

• कोर्स में पाँच अध्याय हैं। = The course has five chapters.
• पैकेज में नाश्ता है। = Breakfast is included in the package.

सदस्यता means membership.

It comes from:

• सदस्य = member
• -ता = a suffix that makes an abstract noun, often like -ness or -ship

So:

• सदस्य = member
• सदस्यता = membership

Depending on context, it can also sometimes mean subscription, but membership is the most direct meaning here.

Hindi does not use articles the way English does. There is no exact everyday equivalent of a/an/the that must appear in every sentence.

So फ़िटनेस क्लास है can naturally mean:

• there is a fitness class
• there is the fitness class
• the membership includes a fitness class

The context tells you which meaning is intended.

If you want to make one more explicit, you can say:

• सदस्यता में एक फ़िटनेस क्लास है।

That would emphasize one fitness class.

है is the third-person singular form of to be.

Here, the thing being talked about is फ़िटनेस क्लास, which is singular, so Hindi uses है.

Compare:

• सदस्यता में फ़िटनेस क्लास है। = There is a fitness class in the membership.
• सदस्यता में फ़िटनेस क्लासें हैं। = There are fitness classes in the membership.

A useful point: in the present tense, है / हैं show number and person, but not gender.

Usually क्लास is treated as feminine in Hindi.

So you may hear:

• अच्छी क्लास = a good class
• यह क्लास लंबी है। = This class is long.
• क्लास शुरू हुई। = The class started.

In your sentence, that feminine gender does not visibly affect है, because है does not change for gender.

Also, with loanwords, usage can vary a little by speaker, but feminine is the most common treatment for क्लास.

It is understandable and quite natural, but many speakers would also say it a little more explicitly:

• सदस्यता में फ़िटनेस क्लास शामिल है।
• सदस्यता में एक फ़िटनेस क्लास शामिल है।

The word शामिल means included. That version sounds a bit closer to the English idea of includes.

Your original sentence is still fine. It uses a simple there is / is included structure rather than a more explicit includes verb.

Yes. Both spellings can be seen:

• फ़िटनेस
• फिटनेस

The letter फ़ uses a dot called a nukta to show an f sound more clearly. Without the dot, फ traditionally represents an aspirated ph sound, but in modern Hindi writing, many people still use फ for English f words.

So:

• फ़िटनेस is a more precise spelling for the English sound
• फिटनेस is also very common in everyday writing

Hindi often prefers a structure like X में Y है instead of using a direct equivalent of include in simple sentences.

So rather than saying:

• The membership includes a fitness class

Hindi very naturally says:

• In the membership, there is a fitness class

If you do want a more direct included idea, you can use:

• शामिल है = is included

For example:

• सदस्यता में फ़िटनेस क्लास शामिल है।

So the original sentence is simple, idiomatic Hindi, even though it is structured differently from English.