Na dvoře je nový gril.

Because after na when you mean a location (in/on/at somewhere), Czech uses the locative case.

• dictionary form: dvůr = courtyard / yard
• locative singular: dvoře

So:

• na dvoře = in the yard / in the courtyard
• na dvůr would be different: it would suggest motion toward the yard and would use the accusative, as in Jdu na dvůr = I’m going out to the yard.

So in your sentence, the grill is already located there, so na dvoře is correct.

With some places, Czech simply prefers na where English might use in or at.

For dvůr / courtyard / yard, the usual expression is:

• na dvoře = in the yard / in the courtyard

This is something you often just have to learn with the noun. Czech prepositions do not always match English ones exactly.

A useful comparison:

• v domě = in the house
• na zahradě = in the garden
• na dvoře = in the yard / courtyard

So na is the natural choice here.

Je is the 3rd person singular form of být (to be).

Here it means is:

• Na dvoře je nový gril.
• There is a new grill in the yard.

Czech often uses je in sentences introducing something that exists somewhere, much like English there is.

Literally, the structure is closer to:

• In the yard is a new grill.

But in natural English, that becomes:

• There is a new grill in the yard.

Nový agrees with gril in gender, number, and case.

• gril is masculine inanimate
• it is singular
• here it is in the nominative case because it is the thing being identified as existing there

So the adjective also takes the nominative masculine inanimate singular form:

• nový gril = new grill

Compare:

• nová lampa = a new lamp
• nové auto = a new car
• nový gril = a new grill

Because gril is the main noun being stated or identified in the sentence.

In a sentence like this:

• Na dvoře je nový gril.

the phrase na dvoře gives the location, and nový gril is what is there. That noun phrase stays in the nominative.

So:

• na dvoře = locative after a preposition
• nový gril = nominative subject-like noun phrase

Even though English uses there is, Czech does not need a separate word like there for this structure.

Yes. Czech word order is fairly flexible, although different orders sound slightly different in emphasis.

Your sentence:

• Na dvoře je nový gril.

is very natural if you are setting the scene first: In the yard, there is a new grill.

Other possible orders:

• Nový gril je na dvoře.
  This puts more focus on the new grill itself.

• Je na dvoře nový gril.
  Possible, but less neutral in everyday use.

Czech often puts known or setting information earlier, and newer or more important information later. So Na dvoře je nový gril sounds very natural.

The hardest part for many learners is ř.

Very roughly:

• dvoře sounds something like dvo-rzheh, but that is only an approximation.

A few points:

• dv at the start is like English dv in advice across a word boundary
• o is a short o
• ř is the famous Czech sound, something between r and zh
• final e is pronounced, not silent

If you cannot say ř yet, a temporary approximation with something like rzh is understandable. Many learners do this at first.

It is a borrowed word, ultimately corresponding to English grill, but in Czech it behaves like a normal masculine noun:

• ten gril = the grill
• nový gril = a new grill

Its spelling is slightly different from English:

• English: grill
• Czech: gril

This is common in Czech: borrowed words are often adapted to Czech spelling and grammar.

Usually gril means a grill, often the cooking device itself. In everyday context, nový gril would normally be understood as a new barbecue grill or grilling appliance, depending on the situation.

If the sentence is about a house, yard, or outdoor space, most people will probably imagine a barbecue grill.

So the exact image depends on context, but the grammar of the sentence stays the same.

You would normally negate je:

• Na dvoře není nový gril.

This means:

• There isn’t a new grill in the yard.

A useful pattern:

• je = is
• není = is not

So:

• Na dvoře je nový gril. = There is a new grill in the yard.
• Na dvoře není nový gril. = There isn’t a new grill in the yard.