zhè jiā jiǔdiàn yǒu hěnduō shèshī.

家 is the measure word here. In Mandarin, when you say this/that + noun, you usually need a measure word in between:

这 + measure word + noun

So:

• 这家酒店 = this hotel

For businesses and establishments such as hotels, restaurants, shops, and companies, 家 is a very common measure word.

So 这家酒店 sounds natural, while 这酒店 is generally not standard.

Here, 有 means to have.

So the sentence structure is:

• 这家酒店 = this hotel
• 有 = has
• 很多设施 = many facilities

So the full idea is This hotel has many facilities.

In other sentences, 有 can also mean there is/there are, but here it clearly means has because the subject is this hotel.

很多 means many or a lot of, and in Mandarin it goes before the noun it modifies:

• 很多设施 = many facilities

That is normal Mandarin word order.

So the phrase is built like this:

• 很多 = many
• 设施 = facilities

Together: many facilities

Usually, no.

You normally say:

• 很多设施

not:

• 很多个设施

With 很多, Mandarin often does not use an extra measure word. Adding one is sometimes possible for emphasis on individual items, but in this sentence it would sound unnecessary and less natural.

Mandarin nouns usually do not change form for singular and plural the way English nouns do.

So 设施 can mean either:

• facility
• facilities

The context tells you which one is meant.

Here, because of 很多 (many), it is clearly plural: facilities.

You may hear 这个酒店 in casual speech, but 这家酒店 is the more natural and standard choice.

Why?

Because 家 is the proper measure word for a hotel as an establishment or business.

So:

• 这家酒店 = more idiomatic / more natural
• 这个酒店 = understandable, but less precise

If you want to sound more native-like, use 这家酒店.

Not very different in this sentence.

The order is:

• 这家酒店 = this hotel
• 有 = has
• 很多设施 = many facilities

So it matches English quite closely:

This hotel has many facilities.

The main extra thing for English speakers is that Mandarin needs the measure word 家 inside this hotel.

Because 有 is the main verb, and it already expresses the idea you need.

Use 是 when linking one noun to another:

• 他是老师。 = He is a teacher.

Use 有 when talking about possession or existence:

• 这家酒店有很多设施。 = This hotel has many facilities.

So 是 would not fit this sentence.

They are related, but not the same.

• 设施 = facilities, amenities, built features, services available
• 设备 = equipment, machines, devices, gear

For a hotel, 设施 is the better word if you mean things like:

• a gym
• a pool
• parking
• elevators
• business center
• laundry service

If you were talking about specific machines or technical hardware, 设备 would be more likely.

The tones are:

• 这 zhè — 4th tone
• 家 jiā — 1st tone
• 酒店 jiǔdiàn — 3rd tone + 4th tone
• 有 yǒu — 3rd tone
• 很多 hěnduō — 3rd tone + 1st tone
• 设施 shèshī — 4th tone + 1st tone

A full reading is:

zhè jiā jiǔdiàn yǒu hěnduō shèshī

In natural speech, some 3rd tones are not pronounced as full dipping tones unless they are stressed or at the end of a phrase. So the sentence may sound smoother and lighter than the dictionary tones suggest.

Historically, the parts are:

• 酒 = alcohol / wine
• 店 = shop / store / establishment

But as a modern word, 酒店 simply means hotel. You should learn it as one vocabulary item, not by translating each character literally in this sentence.

This is common in Chinese: the original character meanings may not match the exact modern meaning of the full word.