من باید آدرس و شماره ساختمان را دوباره بخوانم تا دفتر همکارم را پیدا کنم.

Yes, من can be omitted in normal speech and writing, because the verb ending already shows the subject:

• بخوانم = I read / I should read
• پیدا کنم = I find / I should find

So باید آدرس و شماره ساختمان را دوباره بخوانم... is perfectly natural.

Including من adds emphasis, contrast, or clarity, for example:

• من باید بخوانم، نه تو.
  I have to read it, not you.

In this sentence, من is optional.

باید means must, have to, or should, depending on context.

In this sentence, it expresses necessity:

• من باید ... بخوانم
  I have to / need to read ...

A very common pattern in Persian is:

• باید + subjunctive verb

So:

• باید بخوانم = I must read
• باید پیدا کنم = I must find

Even though English often uses to after have to, Persian does not use a separate word for to here.

After باید, Persian normally uses the subjunctive form, not the regular present indicative.

Compare:

• می‌خوانم = I read / I am reading
• بخوانم = that I read / I should read / I may read

So:

• باید بخوانم = I have to read

This is one of the most important patterns in Persian grammar:

• باید بروم = I must go
• باید ببینم = I must see
• باید پیدا کنم = I must find

را marks a specific direct object.

Here, the direct object is the whole phrase:

• آدرس و شماره ساختمان را
  the address and the building number

So را comes after the entire object phrase, not after each noun separately.

This is very common in Persian:

• کتاب را خواندم = I read the book
• اسم و شماره تلفن او را نوشتم = I wrote down his name and phone number

In your sentence, the speaker has a specific address and a specific building number in mind, so را is natural.

Because the two nouns form one coordinated object:

• آدرس و شماره ساختمان

Persian usually places را once, after the whole direct object phrase:

• آدرس و شماره ساختمان را

This works like saying:

• the address and the building number as one combined object.

You do not normally say:

• آدرس را و شماره ساختمان را

unless you are being especially emphatic or stylistically marked.

Literally, it means:

• شماره = number
• ساختمان = building

So شماره ساختمان means the building number.

This is a noun + noun construction where the first noun is defined by the second. In English, we often translate it in reverse order:

• شماره تلفن = phone number
• شماره اتاق = room number
• شماره ساختمان = building number

Depending on context, this could refer to the number of the building in an address.

This is because Persian often uses the ezafe construction, and in writing it is often not shown after consonants.

So these are pronounced approximately as:

• شمارهِ ساختمان → shomâre-ye sâkhtemân
• دفترِ همکارم → daftar-e hamkâram

The ezafe links nouns to nouns, nouns to adjectives, and so on.

So:

• شماره ساختمان = number of the building
• دفتر همکارم = office of my colleague

Even though you do not see a separate word, the connection is there grammatically.

دوباره means again.

Here it modifies بخوانم:

• دوباره بخوانم = read again

Its position is fairly flexible, but this placement is very natural:

• آدرس و شماره ساختمان را دوباره بخوانم

You may also hear:

• دوباره آدرس و شماره ساختمان را بخوانم

Both are understandable, but the original version sounds very natural.

Here تا means so that, in order to, or so that I can.

It introduces a purpose clause:

• ... دوباره بخوانم تا دفتر همکارم را پیدا کنم
• ... read again so that I can find my colleague’s office

This structure is very common:

• درس می‌خوانم تا قبول شوم
  I study so that I pass.
• زود رفتم تا او را ببینم
  I went early so that I could see him.

So in this sentence, the reading is done for a purpose: finding the office.

Because after تا in a purpose clause, Persian commonly uses the subjunctive.

So:

• تا ... پیدا کنم = so that I find / so that I can find

This matches the idea of intention or goal, not a simple statement of fact.

Compare:

• او را پیدا می‌کنم = I find / I will find him
• تا او را پیدا کنم = so that I find him / in order to find him

So both بخوانم and پیدا کنم are subjunctive, but for different reasons:

• بخوانم because of باید
• پیدا کنم because of تا

دفتر can mean different things depending on context, including:

• office
• notebook
• sometimes register / ledger

In this sentence, because we are talking about an address and building number, دفتر همکارم clearly means:

• my colleague’s office

So context tells you the correct meaning.

Break it down like this:

• همکار = colleague / coworker
• -م = my

So:

• همکارم = my colleague

This -م is a possessive ending attached directly to the noun.

Other examples:

• دوستم = my friend
• کتابم = my book
• استادم = my teacher

Then:

• دفتر همکارم = my colleague’s office

Yes. پیدا کردن is a very common compound verb meaning to find.

It is made of:

• پیدا = found / apparent / visible
• کردن = to do

In actual use, Persian treats this as one verb unit:

• پیدا می‌کنم = I find
• پیدا کردم = I found
• پیدا کنم = I find / I may find / I should find

Many Persian verbs work this way, with a nonverbal element plus a light verb like کردن, شدن, دادن, etc.

Yes, that is a very natural translation.

A few possible English translations are:

• I need to read the address and building number again so that I can find my colleague’s office.
• I have to reread the address and building number to find my colleague’s office.
• I should read the address and building number again in order to find my colleague’s office.

Since the meaning is already known, the main point for learners is that the Persian sentence expresses necessity + purpose very naturally through:

• باید ... بخوانم
• تا ... پیدا کنم

The overall structure is:

• من = subject
• باید = modal of necessity
• آدرس و شماره ساختمان را = direct object
• دوباره = adverb
• بخوانم = verb
• تا دفتر همکارم را پیدا کنم = purpose clause

So the sentence follows the usual Persian tendency toward SOV word order:

• Subject
• Object
• Verb

And then the purpose clause also ends with its verb:

• دفتر همکارم را پیدا کنم

That final-verb pattern is very typical of Persian.