Это как раз тот адрес, который я записал.

Here это works like this is / it is at the start of an identifying sentence.

So:

• Это адрес. = This is an address.
• Это тот адрес. = This is that address / This is the address.

In Russian, это is very commonly used this way before a noun phrase.

Как раз adds the idea of exactly, just, or precisely.

So:

• Это тот адрес = This is the address
• Это как раз тот адрес = This is exactly the address / This is just the address

It often gives a feeling of correct match:

• Это как раз то, что мне нужно. = This is exactly what I need.

Russian has no articles like the and a, so words like этот and тот are often used where English would simply use the, especially when pointing out a specific known thing.

Here тот адрес means something like:

• that address
• the address in question
• the specific address

In this sentence, тот helps identify the address as a particular one.

Both are possible in some contexts, but they are not exactly the same.

• этот адрес = this address
• тот адрес = that address / the particular address

In Это как раз тот адрес..., тот often sounds more like the very address that..., referring back to something already known, remembered, or mentioned.

So the sentence has the sense: This is exactly the address that I wrote down.

Using этот would feel a bit more directly demonstrative: this address right here.

Который is a relative pronoun, meaning which, that, or who, depending on context.

In this sentence:

• тот адрес = that address
• который я записал = that I wrote down

So который connects the noun адрес with the clause describing it.

Whole structure:

• тот адрес, который я записал
  = the address that I wrote down

Because который has to match the noun it refers to and also show its role inside the relative clause.

It refers to адрес, which is:

• masculine
• singular
• inanimate

Inside the clause который я записал, it is the direct object of записал.

For masculine inanimate nouns, the accusative form is the same as the nominative. So:

• nominative: который
• accusative masculine inanimate: который

That is why you see который, not которого.

If it referred to a masculine animate noun, you would normally get которого in the accusative.

Because тот адрес is the main noun phrase being identified by это.

The basic structure is:

• Это ... адрес = This is ... an address / the address

In this type of sentence, the noun after это is usually in the nominative.

So:

• Это дом.
• Это мой брат.
• Это тот адрес...

Because in Russian, relative clauses introduced by words like который are normally separated by a comma.

So:

• тот адрес, который я записал

This is standard punctuation. It is like separating the address from the describing clause that I wrote down.

Записал is perfective past, which means the action is seen as completed: I wrote it down.

That fits well here, because the speaker is referring to a finished act of writing the address down.

Compare:

• я записал = I wrote down / I jotted down
• я записывал = I was writing down / I used to write down / I did write down with more focus on process or repetition

In this sentence, the completed result matters: this is the address that ended up in the speaker’s notes.

Because past-tense verbs in Russian agree with the gender of the subject if the subject is singular.

So:

• я записал = speaker is male
• я записала = speaker is female

If the speaker is a woman, the sentence would be:

Это как раз тот адрес, который я записала.

Here записал usually means wrote down, noted down, or jotted down.

The verb записать often has the sense of recording something in writing so you do not forget it.

So for an address, phone number, name, etc., записать is very natural.

Yes, Russian word order is fairly flexible, but the original order is the most neutral here.

Standard version:

• Это как раз тот адрес, который я записал.

Possible variations exist, but they may change emphasis:

• Это тот адрес, который я как раз записал.
  This shifts как раз closer to the action and can sound like This is the very address I happened to write down / just wrote down, depending on context.

• Тот адрес, который я записал, — это как раз он.
  More marked and much less neutral.

For learners, the original sentence is the best pattern to remember.

Normally no. Russian usually needs an explicit relative word here.

English can say:

• the address I wrote down

But Russian normally says:

• адрес, который я записал

Leaving out который would sound ungrammatical in standard Russian.

Адрес can mean different kinds of address depending on context:

• street/postal address
• email address
• website address
• sometimes even an address in the sense of a formal speech, though that is a different usage

In this sentence, without more context, it most naturally means some kind of address the speaker wrote down. The exact type depends on the situation.