أثق بصديقي.

In Arabic, the verb itself usually shows the subject.

أثق is the present-tense verb I trust. The prefix أـ is the marker for I in the present tense, so Arabic does not need a separate word like أنا unless you want emphasis.

So:

• أثق = I trust
• أنا أثق = I trust / I do trust with extra emphasis on I

Because the verb وثق in Modern Standard Arabic normally takes the preposition بـ when you say whom or what you trust.

So Arabic says:

• أثق بصديقي

Literally, this is closer to I trust in my friend, although the natural English translation is simply I trust my friend.

This is a very common thing in Arabic: some verbs require a preposition even when English does not.

In standard Modern Standard Arabic, no.
With this meaning, the normal pattern is:

• وثق بـ
• أثق ب...

So the correct sentence is:

• أثق بصديقي

not:

• أثق صديقي

صديقي means my friend.

It is made of:

• صديق = friend
• ي = my

So Arabic attaches the possessive pronoun directly to the noun instead of using a separate word for my.

Arabic often expresses possession by adding a suffix to the noun.

So instead of two separate words like English my friend, Arabic uses one combined form:

• صديق = friend
• صديقي = my friend

Other similar examples:

• كتابي = my book
• بيتي = my house

Good question. The root is indeed و ث ق, and the past tense is:

• وَثِقَ = he trusted

But in the present tense, for this type of verb, the initial و drops. So you get:

• يَثِقُ = he trusts
• أَثِقُ = I trust

This is a normal pattern for some verbs with an initial weak letter like و.

Because short prepositions like بـ attach directly to the following word in Arabic spelling.

So:

• بـ
  • صديقي → بصديقي

Even though it is written together, you can still think of it grammatically as:

• بـ = with / in / by, depending on context
• صديقي = my friend

Here, together, it means in my friend in a literal grammatical sense, but naturally my friend after the verb trust.

Yes, partly.

After the preposition بـ, the noun is in the genitive case. Prepositions in Arabic normally make the following noun genitive.

In this sentence, however, the noun also has the suffix ـي meaning my, so the ending already sounds like -ī:

• بِصَدِيقِي

So learners may not notice the case as clearly here, but grammatically the noun after بـ is still genitive.

No, not usually.

أثق بصديقي is already a complete sentence meaning I trust my friend.

You can add أنا if you want emphasis, contrast, or clarity:

• أنا أثق بصديقي = I trust my friend / As for me, I trust my friend

But in normal Arabic, the verb alone is often enough to show the subject.

A careful pronunciation is:

ʾathiqu bi-ṣadīqī

A few helpful sound notes:

• ث sounds like th in think
• ص is a heavier, emphatic s
• ق is a deep q sound, not the English k

So an English-friendly approximation would be something like:

a-thi-qu bi-sa-dee-qee

That approximation is not perfect, but it helps you get started.

Because normal Arabic writing usually leaves out short-vowel marks.

So the fully vocalized form would be:

• أَثِقُ بِصَدِيقِي

But in ordinary texts, it is usually written without those marks:

• أثق بصديقي

Learners often need to know the word already, or infer the vowels from grammar and context.

You can add لا before the present-tense verb:

• لا أثق بصديقي = I do not trust my friend

This is the normal straightforward negation in Modern Standard Arabic for a present-tense meaning.