Гипс на ноге мешает мне быстро ходить.

Гипс is the subject of the sentence, so it stays in the nominative case.

• гипс = the cast / plaster cast
• It is the thing that is causing the problem

So in Гипс на ноге мешает мне быстро ходить, the cast is what hinders or prevents the speaker from walking quickly.

In everyday Russian, гипс can mean both:

• gypsum / plaster as a material
• a medical cast

In this sentence, it clearly means a cast on the leg.

So гипс на ноге means a cast on the leg.

Because на ноге describes location: the cast is on the leg.

After на, Russian uses:

• Prepositional case for location
  
  • на ноге = on the leg
• Accusative case for motion toward something
  
  • на ногу = onto the leg

Here there is no movement. The cast is already there, so Russian uses на ноге.

Russian often omits possessive words like my, your, his, etc. when the meaning is obvious from context.

Here, мне already tells us that the cast is affecting me, so на ноге is naturally understood as on my leg.

Compare:

• Гипс на ноге мешает мне быстро ходить.
  = The cast on my leg prevents me from walking quickly.
• Гипс на моей ноге мешает мне быстро ходить.
  = also correct, but more explicit and a bit heavier

Russian often prefers the shorter version.

Because the verb мешать takes the person affected in the dative case.

Pattern:

• что-то мешает кому-то делать что-то
  = something prevents / hinders someone from doing something

So:

• мешает мне = hinders me
• мне is the dative form of я

Other examples:

• Шум мешает мне работать.
  = The noise prevents me from working.
• Дождь мешает нам гулять.
  = The rain stops us from taking a walk.

After мешать, Russian often uses an infinitive to say what action is being made difficult.

Pattern:

• мешать кому-то + infinitive

So:

• мешает мне быстро ходить
  = makes it hard for me to walk quickly

This is very natural Russian.

You could think of the structure as:

• The cast hinders me
  • in walking quickly

But Russian expresses that with мешает мне быстро ходить.

This is a very common question.

Russian uses:

• идти = to be going, to walk in one specific direction / at one specific time
• ходить = to walk in general, to be able to walk, to walk habitually or repeatedly

Here the sentence is about general ability, not one particular trip. The cast makes walking quickly difficult in general, so ходить is the natural choice.

Compare:

• Гипс на ноге мешает мне быстро ходить.
  = The cast makes it hard for me to walk quickly.
  (general ability)
• Гипс на ноге мешает мне быстро идти.
  = The cast is preventing me from going quickly right now / in this specific instance.
  (more specific, less neutral here)

So ходить is the better default in this sentence.

Мешать means something like:

• to hinder
• to interfere with
• to prevent
• to make it hard

It does not always mean an absolute impossibility. Often it means that something makes the action difficult.

So this sentence can mean:

• the cast prevents me from walking quickly
• the cast makes it hard for me to walk fast

It suggests difficulty, not necessarily total inability.

Because быстро is an adverb modifying ходить:

• быстро ходить = to walk quickly

This is the most neutral word order.

Russian word order is flexible, so other versions are possible, for example:

• Гипс на ноге мешает мне ходить быстро.

This is also understandable, but быстро ходить sounds more natural and compact here.

Yes. Russian word order is flexible, and changing it changes the emphasis, not the core meaning.

For example:

• Гипс на ноге мешает мне быстро ходить.
  Neutral.
• Мне мешает быстро ходить гипс на ноге.
  More emphasis on me or on the fact that walking quickly is difficult for me.
• Быстро ходить мне мешает гипс на ноге.
  Emphasis on walking quickly

The original sentence is the most natural neutral phrasing.

Ноге is the prepositional singular form of нога.

• нога = leg
• на ноге = on the leg

A useful detail: for many feminine nouns, the dative singular and prepositional singular look the same:

• к ноге = to the leg (dative)
• на ноге = on the leg (prepositional)

So even though the form is the same, the case here is prepositional because it follows на in a location meaning.

The stress is:

• ги́пс
• на ноге́
• меша́ет
• мне
• бы́стро
• ходи́ть

So the whole sentence is pronounced roughly:

Ги́пс на ноге́ меша́ет мне бы́стро ходи́ть.

Knowing the stress is useful because Russian stress is not always predictable.

Yes. That is a very natural English translation.

Depending on style, you could translate it as:

• The cast on my leg prevents me from walking quickly.
• The cast on my leg makes it hard for me to walk fast.
• The cast on my leg keeps me from walking quickly.

All of these match the Russian well. The exact English wording can vary, but the grammar of the Russian sentence stays the same.