אני חושבת שהמפתחות שלי אצלך.

Because the speaker is female.

In Hebrew, the present tense often agrees with the gender and number of the subject.
So:

• אני חושבת = I think (said by a woman)
• אני חושב = I think (said by a man)

Even though English just says I think for everyone, Hebrew makes this distinction.

A male speaker would say:

אני חושב שהמפתחות שלי אצלך.

The only change is:

• חושבת → feminine singular
• חושב → masculine singular

Everything else stays the same.

ש־ means that.

So:

• אני חושבת = I think
• שהמפתחות שלי אצלך = that my keys are with you / at your place

In Hebrew, this ש־ is attached directly to the next word, so you get:

• ש + המפתחות → שהמפתחות

This is very common in everyday Hebrew.

Because in present-tense Hebrew, the verb to be is usually omitted.

In English, you say:

• My keys are with you

In Hebrew, you normally just say:

• המפתחות שלי אצלך

Literally, that is closer to:

• the keys שלי with-you / at-your-place

This is completely normal Hebrew.
If you wanted to express were or will be, then Hebrew would usually use forms of להיות.

Hebrew usually expresses possession with של.

So instead of a structure like English my keys, Hebrew commonly says:

• המפתחות שלי = literally the keys of me

This is the normal everyday pattern:

• הספר שלי = my book
• החברים שלי = my friends
• המפתחות שלי = my keys

So שלי means mine / of me.

Because in Hebrew, possessed nouns are often made definite.

So:

• מפתחות = keys
• המפתחות = the keys
• המפתחות שלי = my keys

This may feel strange to an English speaker, because English usually does not say the my keys. But in Hebrew, ה־ with a possessive phrase like שלי is very normal.

אצלך literally means something like at your place, with you, or in your possession.

In this sentence, it suggests:

• the keys are with you
• or you have them
• or they are at your place

It is often used for things that are in someone’s possession or located with them.

Examples:

• הספר אצלך = the book is with you / you have the book
• אני אצלך = I am at your place

So אצלך is a very natural choice here.

Good question. Both can sometimes be translated as with you, but they are not the same.

• אצלך = at your place / in your possession
• איתך = with you, together with you

So in this sentence:

• המפתחות שלי אצלך means my keys are in your possession / at your place

If you said המפתחות שלי איתך, it could also be understood in some contexts, but אצלך is usually more natural when talking about where an object is being kept.

Because Hebrew has some nouns with irregular plural patterns.

• מפתח = key (masculine singular)
• מפתחות = keys (masculine noun with a plural ending that looks feminine)

Usually:

• masculine plural often ends in ־ים
• feminine plural often ends in ־ות

But not always. מפתח is one of those nouns that are masculine even though the plural is מפתחות.

So you should learn its gender separately from its plural ending.

It comes from אצל plus a pronoun ending.

Here are some common forms:

• אצלי = with me / at my place
• אצלך = with you / at your place (to a man)
• אצלך = with you / at your place (to a woman)
  
  • same spelling, different pronunciation in careful speech
• אצלו = with him / at his place
• אצלה = with her / at her place
• אצלנו = with us / at our place
• אצלם / אצלן = with them / at their place

So אצלך is a preposition with a suffix attached.

Yes, very normal.

The sentence is:

• אני חושבת = I think
• שהמפתחות שלי = that my keys
• אצלך = are with you / are at your place

This is a natural Hebrew structure. Hebrew often puts the location or possession phrase directly after the noun phrase, especially in present-tense sentences without to be.

So the sentence sounds natural and idiomatic.

Yes, very often.

Even though the wording is literally closer to I think my keys are with you, the practical meaning in conversation can be:

• I think you have my keys
• I think my keys are at your place
• I think my keys are with you

Which exact English translation fits best depends on context. Hebrew אצלך allows that kind of flexibility.