Cette chaussure me fait mal au pied.

Because chaussure is a feminine singular noun.

French demonstratives change to match the noun:

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

So:

• ce livre = this book
• cet homme = this man
• cette chaussure = this shoe
• ces chaussures = these shoes

Faire mal à quelqu’un means to hurt someone / to cause pain to someone.

In Cette chaussure me fait mal au pied:

• cette chaussure = the subject
• fait = does / makes / causes
• me = to me
• mal = pain / badly

So the structure is basically:

This shoe causes pain to me in the foot.

That is why French uses faire mal here instead of building the sentence exactly like English.

Because me is the object pronoun used before the verb.

French object pronouns usually come before the conjugated verb:

• Il me parle. = He talks to me.
• Cette chaussure me fait mal. = This shoe hurts me.

Moi is a stressed pronoun, used in other situations, for example:

• Moi, je préfère marcher.
• C’est pour moi.

So here, me is the normal form.

French often uses the definite article with body parts when the person is already shown by a pronoun.

So instead of saying to my foot, French often says literally to the foot, while making clear whose foot it is through me:

• Je me lave les mains. = I wash my hands.
• Il me fait mal à la tête. = It gives me a headache / It hurts my head.
• Cette chaussure me fait mal au pied. = This shoe hurts my foot.

So me already tells us whose foot it is, and French does not usually need mon here.

Because the sentence is talking about one foot.

A single shoe often hurts one foot, so au pied is natural.

If the idea were that the shoes hurt both feet, you could say:

• Ces chaussures me font mal aux pieds.

Compare:

• Cette chaussure me fait mal au pied. = This shoe hurts my foot.
• Ces chaussures me font mal aux pieds. = These shoes hurt my feet.

So the singular or plural depends on the real situation.

Because à + le contracts to au in French.

So:

• à + le = au
• à + les = aux

That is why:

• à le pied becomes au pied
• à les pieds becomes aux pieds

This is a normal mandatory contraction in French.

Because avoir mal and faire mal do different jobs.

• avoir mal = to be in pain
• faire mal à = to hurt / to cause pain to

So:

• J’ai mal au pied. = My foot hurts / I have pain in my foot.
• Cette chaussure me fait mal au pied. = This shoe hurts my foot.

The first sentence focuses on your pain. The second focuses on the shoe as the cause.

Yes, that is possible, but it means something slightly different in focus.

• Cette chaussure me fait mal au pied.
  Focus: the shoe is causing the pain

• J’ai mal au pied avec cette chaussure.
  Focus: I have foot pain when I wear this shoe

Both are natural, but the original sentence is more direct when you want to blame the shoe itself.

Chaussure here means one shoe.

French can use:

• une chaussure = one shoe
• des chaussures = shoes

So the original sentence is talking about a single shoe.

If you wanted to talk about both shoes, you would normally use the plural:

• Ces chaussures me font mal aux pieds.

Because the subject is singular: cette chaussure.

The verb agrees with the subject:

• Cette chaussure me fait mal... = singular subject → fait
• Ces chaussures me font mal... = plural subject → font

So fait matches cette chaussure.

No, here mal works more like a noun or fixed part of the expression faire mal.

You should learn faire mal à as a set expression meaning:

• to hurt
• to cause pain

So it is better not to analyze it too literally as ordinary badly.

Examples:

• Ça fait mal. = That hurts.
• Il me fait mal au bras. = He is hurting my arm.
• Ces chaussures font mal. = These shoes hurt.

Because in French, object pronouns usually come before the conjugated verb.

That is a basic French word-order rule.

Examples:

• Il me voit. = He sees me.
• Elle nous parle. = She talks to us.
• Cette chaussure me fait mal. = This shoe hurts me.

English puts these after the verb, but French usually puts them before it.

Yes. In normal usage, that idea is understood.

When someone says:

Cette chaussure me fait mal au pied

the natural interpretation is:

This shoe hurts my foot when I wear it.

French often leaves that context unstated because it is obvious from the situation.

You would make everything plural where needed:

Ces chaussures me font mal aux pieds.

Changes:

• cette → ces
• chaussure → chaussures
• fait → font
• au pied → aux pieds

That gives the natural plural version.