Страх мешает ему спать.

It breaks down like this:

• страх — subject, nominative singular
• мешает — verb, 3rd person singular present
• ему — dative form of он, meaning to him
• спать — infinitive, to sleep

A very common Russian pattern is:

что-то мешает кому-то делать что-то

= something prevents/hinders someone from doing something

So this sentence is built very normally.

Because the verb мешать normally takes the dative case for the person affected.

So:

• ему = to him
• его = him / his in other grammatical roles

With мешать, Russian asks basically What is bothering/interfering with whom?

• Страх мешает ему спать = Fear interferes with him sleeping

So ему is required by the verb.

Because after мешать, Russian often uses an infinitive to say what action is being prevented.

So:

• мешает ему спать = prevents him from sleeping
• literally, something like hinders him to sleep, though that is not natural English

This is a standard Russian construction:

• Мама мешает мне работать = Mom is preventing me from working
• Шум мешает детям спать = Noise keeps the children from sleeping

Russian does not need a separate word here.

In English, we say:

• prevent someone from doing something

In Russian, the idea is built into the pattern:

• мешать кому-то + infinitive

So мешает ему спать already means prevents him from sleeping / keeps him from sleeping. There is no missing preposition.

Мешает is the 3rd person singular present tense form of мешать.

It agrees with страх, which is singular:

• страх мешает = fear hinders
• not мешают, because that would be plural

The ending -ет here tells you it is he/she/it in the present tense.

Yes, those are possible in other contexts, but they mean something different.

• мешать = imperfective, ongoing/general/repeated interference
• помешать = perfective, a single completed act of interference

So:

• Страх мешает ему спать = Fear is preventing him from sleeping / Fear keeps him from sleeping
• Страх помешал ему уснуть = Fear prevented him from falling asleep
• Страх помешает ему работать = Fear will prevent him from working

In your sentence, the imperfective sounds natural because it describes an ongoing state.

Yes. Russian word order is more flexible than English.

The neutral version is:

• Страх мешает ему спать

But you could also say:

• Ему мешает спать страх
• Спать ему мешает страх

These all mean roughly the same thing, but the emphasis changes.

• Страх мешает ему спать — neutral
• Ему мешает спать страх — emphasizes him
• Спать ему мешает страх — emphasizes sleeping

So the original sentence is a normal, straightforward order.

Russian has no articles like a or the, so страх can mean:

• fear
• a fear
• the fear

The exact meaning depends on context.

In this sentence, it could mean:

• fear in general
• his fear
• a specific fear already mentioned

English forces you to choose more often; Russian often leaves that to context.

Here спать means to sleep.

If you want specifically to fall asleep, Russian often uses уснуть:

• Страх мешает ему уснуть = Fear prevents him from falling asleep

So there is a useful distinction:

• спать = to be sleeping / to sleep
• уснуть = to fall asleep

Your original sentence suggests that fear is interfering with sleep generally, not necessarily only the moment of falling asleep.

Yes. A very common alternative is:

• Страх не даёт ему спать

Literally: Fear does not give him sleep Naturally: Fear won’t let him sleep / Fear keeps him awake

Compared with мешает, не даёт often sounds a bit more everyday and direct.

So both are natural:

• Страх мешает ему спать — fear interferes with his sleeping
• Страх не даёт ему спать — fear won’t let him sleep

A simple pronunciation guide:

• страх — strah
• мешает — mee-SHA-yet
• ему — yee-MOO
• спать — spaht’

Stress:

• страх
• мешает
• ему
• спать

So the whole sentence sounds roughly like:

strah mee-SHA-yet yee-MOO spaht’

One small point: the ш in мешает is a hard sh sound, not soft.