Tento druh služby je levný.

Both are possible, but they are slightly different in style.

• tento = this, and it is a bit more explicit or careful
• ten can also mean this/that depending on context, and is very common in everyday speech

So Tento druh služby is a clear, standard way to say this kind of service.

In conversation, many speakers might also say:

• Tenhle druh služby je levný.

That is more colloquial.

The whole phrase is in the nominative, because it is the subject of the sentence.

The main noun in the subject is druh. That is why:

• tento agrees with druh
• levný also agrees with druh

Inside that phrase, služby is in a different case, because it depends on druh.

So the structure is:

• tento druh = nominative singular
• služby = genitive singular

Because druh often takes a noun in the genitive to mean a kind/type of something.

So:

• druh služby = a kind of service
• literally, something like type of service

This is a very common pattern in Czech:

• druh zboží = type of goods
• typ auta = type of car
• sklenice vody = glass of water

So after druh, the thing being classified is usually in the genitive.

Because levný agrees with druh, not with služba.

The noun druh is masculine inanimate singular, so the adjective must also be masculine singular:

• druh → masculine
• levný → masculine form

Even though služba is feminine, it is not the main noun of the sentence here. It is only part of the genitive phrase druh služby.

So Czech grammar treats the sentence as if it were saying:

• This kind is cheap
• specifically, this kind of service is cheap

Druh is a masculine inanimate noun.

That matters because it controls agreement:

• tento druh
• je levný

If it were feminine, you would expect forms like tato and levná, but that is not what happens here because the head noun is masculine.

Yes, but it means something slightly different.

• Tato služba je levná. = This service is cheap.
• Tento druh služby je levný. = This kind/type of service is cheap.

The second sentence is more general. It talks about a category or type of service, not one specific service instance.

So the difference is:

• služba = the service itself
• druh služby = the kind/type of service

Yes, in a normal present-tense sentence like this, je is needed.

Czech usually keeps the verb být in the present tense in this kind of sentence:

• Tento druh služby je levný.

You cannot normally omit je the way Russian sometimes omits to be in the present.

So je is the standard and correct form here.

Because Czech has no articles.

English uses:

• a kind
• the kind
• this kind

Czech does not have separate words like a or the. Instead, it uses context, word order, and demonstratives like tento when needed.

So:

• druh služby can mean a kind of service or the kind of service, depending on context
• tento druh služby clearly means this kind of service

Yes, Czech word order is flexible, but the neutral order here is:

• Tento druh služby je levný.

Other word orders are possible for emphasis, for example:

• Levný je tento druh služby.
• Tento druh služby levný je.

But these sound marked or emphatic in most contexts. A learner should generally use the neutral order unless there is a special reason to emphasize something.

Levný is the normal neutral word for cheap or inexpensive.

It usually means low in price and does not automatically sound negative.

There is also laciný, which can mean cheap, but it often suggests cheap in a bad way, like low-quality, tacky, or inferior.

So:

• levný = inexpensive
• laciný = cheap in a more negative sense

In your sentence, levný is the natural choice.

Good question, because the form služby can mean more than one thing depending on context.

It can be:

• genitive singular of služba
• nominative plural of služba
• accusative plural of služba

Here it must be genitive singular, because it follows druh in the pattern druh + genitive.

So the grammar of the sentence tells you how to interpret it.

They are similar, and in many contexts both can mean kind/type.

• druh often means kind, species, sort
• typ often means type

In everyday language, both can be used in many similar situations:

• druh služby
• typ služby

But they are not always identical in every context. Druh can sometimes feel a bit broader or more traditional, while typ can feel more technical or classificatory.

In this sentence, druh služby sounds perfectly natural.