Puella timet ne canis eam laedat.

In a fear clause, ne often means that rather than simple not.

So after a verb of fearing like timet (she fears), Latin uses:

• ne = that / that ... might
• ut = that ... not

So:

• Puella timet ne canis eam laedat = The girl fears that the dog may hurt her
• If Latin wanted to say The girl fears that the dog will not hurt her, it would typically use ut, not ne

This feels backward to English speakers at first, but it is standard Latin idiom.

Because it is in a subordinate clause after a verb of fearing.

Latin regularly uses the subjunctive in fear clauses. Here:

• timet = main verb
• ne canis eam laedat = fear clause
• laedat = present subjunctive

So the subjunctive is not random; it is required by the grammar of the clause.

Laedit is indicative: he/she/it hurts.

Laedat is subjunctive: he/she/it may hurt, or more literally the verb form used in this kind of dependent clause.

Since this sentence contains a fear clause introduced by ne, Latin uses the subjunctive:

• laedit = not correct here for normal classical prose
• laedat = correct

This is because of sequence of tenses.

The main verb is timet, which is present. A present main verb is a primary tense, so Latin normally uses:

• present subjunctive for action happening at the same time as the main verb or after it
• perfect subjunctive for action completed before the main verb

Here the girl is afraid of something that may happen now or in the future, so Latin uses the present subjunctive:

• timet ... laedat

If the main verb were past, you would often expect the imperfect subjunctive:

• Puella timebat ne canis eam laederet
  The girl was afraid that the dog might hurt her

Here canis is nominative singular, the subject of laedat.

So the structure is:

• canis = the dog = subject
• eam = her = direct object
• laedat = may hurt

Even though canis can look the same in nominative and genitive singular in dictionaries, in this sentence it must be nominative because it is the one doing the action.

Eam is accusative singular feminine.

It is the direct object of laedat, so it means her.

It refers back to puella:

• Puella = the girl
• eam = her

Latin often uses a pronoun like this when the person in the subordinate clause is the same one already mentioned in the main clause.

It could repeat the noun in some contexts, but using eam is natural and efficient.

Compare:

• Puella timet ne canis eam laedat = The girl fears that the dog may hurt her
• repeating the noun would be less elegant and less natural in ordinary prose

Latin often prefers a pronoun when the reference is already clear.

Because se is a reflexive pronoun, and reflexives normally refer back to the subject of their own clause.

In the subordinate clause:

• canis is the subject
• so se would refer to the dog

That would give the meaning:

• The girl fears that the dog may hurt itself

But the sentence means the dog may hurt the girl, so Latin uses eam, not se.

A helpful breakdown is:

• Puella = the girl
• timet = fears
• ne = that / that ... might
• canis = the dog
• eam = her
• laedat = may hurt

So the structure is:

• main clause: Puella timet
• subordinate clause: ne canis eam laedat

Latin word order is more flexible than English because the endings show the grammar. Still, placing the verb at the end of the subordinate clause, as here, is very common.

Yes. Canis can be masculine or feminine depending on the actual dog.

So this sentence could mean:

• The girl fears that the male dog may hurt her
• or The girl fears that the female dog may hurt her

Latin does not mark the gender clearly in canis itself here. You would know from context if it mattered.

Yes.

Puella is singular, so the verb must also be singular:

• puella = girl
• timet = she fears

If the subject were plural, the verb would change:

• Puellae timent ne canis eas laedat
  The girls fear that the dog may hurt them

Very literal would be something like:

• The girl fears lest the dog hurt her
• or The girl fears that the dog may hurt her

In more natural English, you might also say:

• The girl is afraid that the dog will hurt her

The Latin grammar is not exactly the same as English grammar, but that is the sense.

No. It is specifically a fear clause.

Even though ne + subjunctive can appear in several constructions, you identify this one by the main verb timet, a verb of fearing.

So:

• after verbs of fearing, ne + subjunctive = fear clause
• in other contexts, ne + subjunctive might be a negative purpose clause, negative command, and so on

The main verb tells you how to understand it here.