Das Bohren im Flur ist heute sehr laut.

Because Bohren is being used as a noun, not as a normal verb.

The verb is bohren = to drill.
When German turns an infinitive verb into a noun, it is capitalized:

• bohren = to drill
• das Bohren = the drilling / drilling

This is similar to English drilling, but in German it is treated more clearly as a noun.

Because in this sentence, Bohren is the subject and is being used as a noun. German normally uses an article with this kind of nominalized infinitive.

• Das Bohren im Flur ist heute sehr laut. = The drilling in the hallway is very loud today.

If you used bohren without das, it would normally be understood as the verb to drill, not the noun drilling.

When an infinitive verb is turned into a noun in German, it is usually neuter, so it takes das.

Examples:

• das Essen = eating / food
• das Schwimmen = swimming
• das Bohren = drilling

So das Bohren is not something you just memorize separately from the verb; it follows a common pattern.

It is singular, so the verb is ist.

Here, das Bohren refers to the activity as one thing:

• Das Bohren ... ist laut. = The drilling ... is loud.

Even if several people are drilling, the sentence is treating the whole activity as a single thing, so German uses singular agreement.

It most naturally means the drilling activity, but in context it can also strongly suggest the noise caused by drilling.

It does not mean the tool itself.
For the tool, German would use something like:

• der Bohrer = the drill / drill bit

So in this sentence, das Bohren means the act of drilling, and because it is described as sehr laut, the focus is really on the noise of that activity.

Im is a contraction of in dem:

• in dem Flur → im Flur

This is extremely common in German.

So:

• im Flur = in the hallway / corridor

German often contracts:

• in dem → im
• an dem → am
• zu dem → zum
• zu der → zur

Because in can take either accusative or dative, depending on meaning:

• accusative for movement toward somewhere
• dative for location

Here there is no movement. The drilling is happening in the hallway as a location, so German uses the dative:

• im Flur = in the hallway

Compare:

• Ich gehe in den Flur. = I go into the hallway. → movement, accusative
• Ich bin im Flur. = I am in the hallway. → location, dative

Because laut comes after ist and works as a predicate adjective. Predicate adjectives in German do not take adjective endings.

So:

• Das Bohren ist laut. = correct
• Das laute Bohren = also correct, but here laute comes before the noun and directly describes it

Compare:

• das laute Bohren = the loud drilling
• das Bohren ist laut = the drilling is loud

This is very similar to English:

• the loud drilling
• the drilling is loud

Because heute is a time expression, and German often places time expressions in the middle of the sentence before information like manner or description.

So:

• Das Bohren im Flur ist heute sehr laut.

This sounds natural as:

• subject: Das Bohren im Flur
• verb: ist
• time: heute
• description: sehr laut

You can think of it as:

• The drilling in the hallway is very loud today.

German word order is flexible, but this order is very normal.

Yes, but the emphasis may change.

For example:

• Heute ist das Bohren im Flur sehr laut.
  = Today, the drilling in the hallway is very loud.
  This puts stronger emphasis on today.

• Das Bohren im Flur ist sehr laut heute.
  This is possible, but less neutral and often sounds more spoken or marked.

The original sentence is a natural, neutral way to say it.

Because German main clauses usually follow the V2 rule: the finite verb comes in the second position.

In this sentence:

• Das Bohren im Flur = first element
• ist = second position
• heute sehr laut = the rest

Even if you move another element to the front, the verb still stays second:

• Heute ist das Bohren im Flur sehr laut.

So the verb is not necessarily the second word, but the second sentence element.

Sometimes, but they do not mean exactly the same thing.

• das Bohren = the activity of drilling
• die Bohrung = a drilling / borehole / drilled opening, often more technical
• die Bohrarbeiten = the drilling work, often plural and more concrete

In your sentence, das Bohren is the most natural choice if you mean the ongoing activity/noise.

For example:

• Die Bohrarbeiten im Flur sind heute sehr laut.
  = The drilling work in the hallway is very loud today.

That is also possible, but it feels a little more specific or formal than das Bohren.

Yes, that is a very helpful way to think about it.

• bohren = to drill
• das Bohren = drilling / the drilling

So das Bohren often corresponds to an English -ing noun form.

But remember: in German it is a proper noun-like form with:

• a capital letter
• usually the article das
• normal noun behavior in the sentence

So it is similar to English drilling, but grammatically more clearly a noun.