هو يحفر ثقبا بالمثقاب في الحائط.

Yes. In Arabic, the verb يحفر already tells you the subject is he (third person masculine singular). So هو is not strictly necessary.

• يحفر = he digs / he is digging / he drills
• هو يحفر = he digs / he is digging

Adding هو can:

• make the subject more explicit
• add emphasis or contrast
• simply sound clearer in a teaching example

So all of these are possible, depending on context:

• يحفر ثقبًا بالمثقاب في الحائط
• هو يحفر ثقبًا بالمثقاب في الحائط

يحفر is from the root ح ف ر and basically means to dig. In context, it can also be understood as to drill, especially when the object is a hole and the instrument is a drill.

So in this sentence, يحفر is being used in the sense of making a hole.

Grammatically, يحفر is:

• imperfect/present tense
• third person
• masculine
• singular

So it can mean:

• he digs
• he is digging
• sometimes he drills, depending on context

Because the sentence means a hole, not the hole.

• ثقبًا / ثقبا = a hole (indefinite)
• الثقب = the hole (definite)

Arabic marks indefiniteness differently from English. Instead of using a word like a, it usually leaves off ال and, in fully vocalized writing, often adds tanwīn.

So ثقبًا means a hole, while الثقبَ would mean the hole.

Because it is the direct object of the verb يحفر.

He is doing the action of digging/drilling, and the thing being produced or affected is a hole. That makes ثقبًا the object, so it takes the accusative case.

Fully vocalized, it is:

• ثُقبًا

You may see it written without short vowels as:

• ثقبا

That final written ا is the normal spelling used with tanwīn fatḥ on many indefinite accusative nouns.

It is very similar to English dig a hole, and yes, that kind of structure is completely normal.

Arabic often uses:

• a verb for the action
• plus a noun for the thing produced or affected

So يحفر ثقبًا is a natural way to say he is digging/drilling a hole.

It is not strange or redundant in Arabic. It works much like English:

• dig a hole
• make a hole

Here بـ means with / by means of and introduces the instrument used to do the action.

So:

• بالمثقاب = with the drill / using the drill

This is a very common use of بـ in Arabic. It often marks the tool or means by which something is done.

Examples of the same idea:

• كتب بالقلم = he wrote with a pen
• قطع بالسكين = he cut with a knife

So here:

• يحفر ... بالمثقاب = he drills/digs ... with a drill

Both are possible, but they are slightly different.

• بالمثقاب = with the drill
• بمثقابٍ = with a drill

Using ال can mean:

• a specific drill already known in the situation
• or sometimes a generic tool of that type, depending on context

So بالمثقاب is not wrong at all. It may suggest:

• with the drill (a particular one)
• or simply the tool being used, in a natural descriptive way

If you wanted to stress with a drill in a more indefinite sense, بمثقابٍ would also be good.

Because the hole is being made in/into the wall, not on the surface of the wall.

• في = in / inside / into (depending on context)
• على = on / on top of

A hole goes into the wall, so في الحائط is the natural choice.

So:

• في الحائط = in the wall / into the wall
• على الحائط would sound more like on the wall, which does not fit the idea of drilling a hole very well

Because it comes after the preposition في.

In Arabic, nouns after prepositions normally take the genitive case.

So:

• في → forces the following noun into the genitive
• الحائطِ = genitive form of الحائط

Likewise, المثقابِ is also genitive because it comes after بـ in بالمثقابِ.

So the case pattern is:

• يحفرُ → verb
• ثقبًا → accusative object
• بالمثقابِ → genitive after بـ
• في الحائطِ → genitive after في

It is the imperfect form, which can cover several meanings in English depending on context.

So يحفر can mean:

• he digs
• he is digging
• he drills
• he is drilling

Arabic does not always separate simple present and present progressive as clearly as English does. Context usually tells you which is meant.

In this sentence, because it describes an ongoing action, English would often translate it as:

• he is drilling a hole...

But grammatically, the Arabic form itself can cover both.

It is natural, but it is not the only possible order.

Arabic allows some flexibility. This sentence begins with the pronoun:

• هو يحفر ثقبا بالمثقاب في الحائط

That gives the sentence a slightly more explicit subject-first feel.

A very common alternative would be:

• يحفر ثقبا بالمثقاب في الحائط

This is also very natural in MSA.

Very roughly:

• starting with هو can emphasize or foreground he
• starting with the verb is often more neutral in formal Arabic

So the sentence as given is fine, but it is not the only correct arrangement.

A fully vocalized version would be:

هُوَ يَحفِرُ ثُقبًا بِالمِثقابِ فِي الحائطِ

A few notes:

• هُوَ = he
• يَحفِرُ = final ـُ because it is the indicative imperfect
• ثُقبًا = accusative, indefinite
• بِالمِثقابِ = genitive after بـ
• فِي الحائطِ = genitive after في

In normal everyday printing, many of these short vowels are omitted, so you often see:

هو يحفر ثقبا بالمثقاب في الحائط

and readers supply the grammar from context.