Mein Vater gräbt mit dem Spaten ein tiefes Loch, damit die Wurzeln genug Platz haben.

Because the subject is Mein Vater, which is third-person singular (he).

The verb graben means to dig. In the present tense, it changes like this:

• ich grabe
• du gräbst
• er/sie/es gräbt
• wir graben
• ihr grabt
• sie/Sie graben

So with mein Vater, you need gräbt.

This is also a stem-vowel changing verb: a changes to ä in the du and er/sie/es forms.

Mein Vater is the subject of the sentence, so it is in the nominative case.

• mein Vater = my father as the doer of the action

If it were a direct object, the form would change:

• nominative: mein Vater
• accusative: meinen Vater

But here he is the one doing the digging, so Mein Vater is correct.

The preposition mit always takes the dative case.

So:

• der Spaten = the spade/shovel-like digging tool
• dative masculine singular becomes dem Spaten

That is why you get:

• mit dem Spaten = with the spade

A quick pattern:

• mit dem Mann
• mit der Frau
• mit dem Kind
• mit den Kindern

Since Spaten is masculine (der Spaten), dem is required after mit.

Der Spaten is a spade, a digging tool. In some contexts, English speakers might also think of shovel, but spade is usually the more precise match here.

So:

• mit dem Spaten = with the spade

It refers to the tool being used to dig the hole.

This is the direct object of gräbt, so it is in the accusative case.

The noun is:

• das Loch = the hole

Because Loch is neuter, and because it is in the accusative singular with ein, the adjective ending is -es:

• ein tiefes Loch

Compare:

• ein tiefer Graben (masculine nominative)
• einen tiefen Graben (masculine accusative)
• eine tiefe Grube (feminine)
• ein tiefes Loch (neuter)

So tiefes is correct because it agrees with Loch.

Because all nouns are capitalized in German.

So in this sentence, words like these are capitalized because they are nouns:

• Vater
• Spaten
• Loch
• Wurzeln
• Platz

This is one of the most noticeable spelling differences between German and English.

Here damit means so that or in order that.

It introduces a purpose clause:

• Mein Vater gräbt ... ein tiefes Loch, damit die Wurzeln genug Platz haben.
• My father is digging a deep hole so that the roots have enough room.

So the second part explains the purpose of digging the hole.

Be careful: damit can also mean with that in other contexts, but not here. In this sentence, it is a subordinating conjunction meaning so that.

Because damit introduces a subordinate clause, and in German subordinate clauses, the conjugated verb goes to the end.

Main clause:

• Mein Vater gräbt mit dem Spaten ein tiefes Loch

Subordinate clause:

• damit die Wurzeln genug Platz haben

In English, word order stays more normal:

• so that the roots have enough room

But in German, after damit, the verb moves to the end:

• damit ... haben

This is a very common rule with subordinating conjunctions such as:

• weil = because
• dass = that
• wenn = if/when
• obwohl = although
• damit = so that

Die Wurzeln means the roots.

The base noun is:

• singular: die Wurzel = the root
• plural: die Wurzeln = the roots

In the clause damit die Wurzeln genug Platz haben, die Wurzeln is the subject, so it is in the nominative plural.

That is why the verb is also plural:

• die Wurzeln haben = the roots have

Because the subject is plural: die Wurzeln.

Compare:

• die Wurzel hat = the root has
• die Wurzeln haben = the roots have

So the verb must match the plural subject.

Genug Platz means enough room or enough space.

Here, Platz is being used in a fairly general, uncountable sense, like room/space in English. That is why there is no article:

• genug Platz = enough space
• viel Platz = a lot of space
• wenig Platz = little space

This is very natural in German.

You could think of it like English:

• The roots need enough space not usually
• the roots need an enough space

So the German structure is normal.

In genug Platz, genug is being used like an indeclinable quantity word, so it does not take adjective endings here.

You simply say:

• genug Platz
• genug Zeit
• genug Geld
• genug Wasser

Not:

• genuger Platz
• genuges Platz

So genug stays the same.

A related alternative is genügend:

• genügend Platz

That also means enough space, but in your sentence genug Platz is the more everyday phrasing.

Yes, German word order in the middle field is somewhat flexible.

The fixed points are:

• the conjugated verb in second position in the main clause: gräbt
• the rest of the sentence comes after that

So this is natural:

• Mein Vater gräbt mit dem Spaten ein tiefes Loch ...

But you could also say:

• Mein Vater gräbt ein tiefes Loch mit dem Spaten ...

Both are possible. The version with mit dem Spaten before ein tiefes Loch sounds very natural because German often places short prepositional phrases before the direct object.

So the sentence order is standard, but not the only possible order.

Not in this sentence as it stands.

Um ... zu is used when the subject of both clauses is the same.

Example:

• Mein Vater gräbt ein tiefes Loch, um einen Baum zu pflanzen.
• My father digs a deep hole in order to plant a tree.

Here, my father is understood as the person doing both actions.

But in your sentence, the second clause has a different subject:

• die Wurzeln have enough space

So you need damit:

• ..., damit die Wurzeln genug Platz haben.

That is the normal choice when the second clause has its own subject.

German present tense often covers both meanings.

So Mein Vater gräbt ... can mean:

• My father is digging ... (right now)
• My father digs ... (general/habitual, depending on context)

German does not require a separate form like English is digging. The exact meaning usually comes from context.

This sentence is a nice example of several case patterns:

• Mein Vater → nominative
  the subject of gräbt

• mit dem Spaten → dative
  because mit always takes dative

• ein tiefes Loch → accusative
  the direct object of gräbt

• die Wurzeln → nominative
  the subject of haben

• genug Platz → accusative-like object meaning after haben
  in practice, you learn it as Platz haben = to have space/room

So the sentence is useful because it shows subject + dative prepositional phrase + accusative object + subordinate clause.

It has two parts:

1. Main clause
   Mein Vater gräbt mit dem Spaten ein tiefes Loch

2. Subordinate clause of purpose
   damit die Wurzeln genug Platz haben

So the overall pattern is:

• Main clause + damit + subordinate clause

This is a very common German structure for expressing purpose:

• Someone does X, damit Y passiert / damit someone can do Y.

In your sentence:

• action: digging a deep hole
• purpose: the roots have enough room