Sans cette pince, il est difficile d’enlever le petit clou.

Because pince is a feminine singular noun.

French demonstrative adjectives change according to gender and number:

• ce = masculine singular before most consonants
• cet = masculine singular before a vowel or mute h
• cette = feminine singular
• ces = plural

So:

• ce clou = this nail
• cette pince = this tool / these pliers

Because cette is already the determiner.

In sans cette pince, sans means without, and cette means this. French does not add another article before a demonstrative adjective.

So you get:

• sans cette pince = without this tool

not something like sans la cette pince, which would be incorrect.

Here, il is an impersonal subject. It does not refer to a person or thing. It works like English it in sentences such as:

• It is difficult to...
• It is important to...

So:

• il est difficile d’enlever le petit clou
  = it is difficult to remove the small nail

The il is just required by French grammar.

Because after expressions like il est difficile, French normally uses de + infinitive.

Pattern:

• il est difficile de + infinitive
• il est facile de + infinitive
• il est important de + infinitive

So:

• il est difficile d’enlever...

This is the normal structure for it is difficult to remove...

This is called elision.

When de comes before a vowel sound, the e drops:

• de enlever → d’enlever

The same thing happens in many common combinations:

• de autres → d’autres
• de accord → d’accord

Since enlever starts with a vowel sound, French uses d’.

Because petit is one of the common adjectives that usually comes before the noun.

In French, many adjectives come after the noun, but some frequent ones often come before it, especially adjectives of:

• beauty
• age
• goodness
• size

This is often remembered with the shorthand BAGS.

Since petit expresses size, it usually goes before the noun:

• le petit clou = the small nail

Pince is a singular French noun for a gripping tool. Depending on context, it can mean things like:

• pliers
• pincers
• tongs
• tweezers

In this sentence, it most likely refers to a tool used to pull out a nail, so pliers is a natural translation in English.

French often uses a singular noun where English may prefer a plural-looking word like pliers. So cette pince can still be translated naturally as these pliers or this pair of pliers, depending on context.

Yes, you could, especially in everyday spoken French.

Both are possible:

• Il est difficile d’enlever le petit clou.
• C’est difficile d’enlever le petit clou.

The version with il est is often a bit more neutral or formal in tone.
The version with c’est is very common in conversation.

So the original sentence is completely natural, but it is not the only possible phrasing.

It is placed first to set the condition or context right away:

• Sans cette pince, il est difficile d’enlever le petit clou.

This is similar to English:

• Without this tool, it is difficult to remove the small nail.

You could also say:

• Il est difficile d’enlever le petit clou sans cette pince.

That is also correct. Putting sans cette pince first gives it a little more emphasis.

When a short introductory phrase is placed at the beginning, French often uses a comma to separate it from the main clause:

• Sans cette pince, il est difficile d’enlever le petit clou.

The comma helps readability and is very natural here.
In a very short sentence, you may sometimes see less punctuation, but in standard writing the comma is a good choice.

Yes. Enlever is a natural choice and means to remove or take out.

For a nail, other verbs are possible depending on nuance:

• retirer = to remove, to take out
• arracher = to pull out forcibly
• ôter = to remove, more formal/literary in some contexts

So:

• enlever le petit clou sounds normal and general
• arracher le petit clou would sound stronger, more forceful

Because noun gender in French is grammatical, not based on natural gender.

Clou is simply a masculine noun, so it takes:

• le clou
• ce clou
• un clou

This is something learners usually just have to memorize with each noun. In this sentence:

• le petit clou = the small nail