Tarkistan sähköpostiosoitteen ja postinumeron varmistaakseni, että tiedot ovat oikein.

Finnish often leaves the subject pronoun out because the verb ending already tells you who is doing the action.
Here, tarkistan ends in -n, which marks 1st person singular, so it already means I check / I am checking.

You could say Minä tarkistan..., but that would usually add emphasis, like I am checking.

It is the present tense. In Finnish, the present tense often covers both:

• I check
• I am checking

So the exact English translation depends on context. Finnish does not have a separate verb form just for the English-style progressive.

They are the objects of tarkistan. In a sentence like this, a singular total object usually appears in a form that looks like the genitive:

• sähköpostiosoite → sähköpostiosoitteen
• postinumero → postinumeron

This suggests the speaker is checking the whole email address and the whole postal code, not just part of them.

They are related, but not the same:

• tarkistaa = to check, inspect, verify
• varmistaa = to make sure, ensure

So the sentence is structured like this:

• I check the email address and postal code
• to make sure that the information is correct

The first verb describes the action itself. The second describes the purpose of that action.

Varmistaakseni means to make sure or more literally in order for me to ensure.

It is built from:

• varmistaa = to ensure / make sure
• -kse- = a purpose element
• -ni = my / I marker here, showing that I am the one doing the ensuring

So:

• varmistaa
• varmistaa + kse + ni
• varmistaakseni

This is a very common Finnish way to express purpose when the subject is the same as in the main clause.

Että means that and introduces a subordinate clause:

• että tiedot ovat oikein
• that the information/details are correct

The comma is there because Finnish normally uses a comma before this kind of subordinate clause. So ..., että ... is standard punctuation.

This is a very common difference between Finnish and English.

• tieto = a piece of information / a fact
• tiedot = information, details, data

In many everyday situations, especially on forms and websites, Finnish uses tiedot where English would simply say information.

So tiedot is plural in form, even though the English translation may sound singular.

Because the subject tiedot is plural.

• tiedot ovat
• the details/information are

If the subject were singular, Finnish would use on instead:

• tieto on oikein = the piece of information is correct

Here, oikein is an adverb, and olla oikein is a common Finnish expression meaning to be correct / to be right.

So:

• tiedot ovat oikein = the information/details are correct

You might also see oikeat, but that gives a slightly different feel:

• tiedot ovat oikeat = the details are the right/correct ones

In this sentence, oikein is the more natural choice for simple correctness.

Yes. Finnish uses compound words very freely.

• sähköposti

  • osoite = sähköpostiosoite
    (email
    • address = email address)

• posti

  • numero = postinumero
    (post/mail
    • number = postal code)

A useful thing to notice is that in a compound noun, the case ending usually goes on the last part:

• sähköpostiosoite → sähköpostiosoitteen

Finnish has no articles, so it does not have separate words for a, an, or the.

Whether something is understood as a or the usually comes from context. So even though Finnish just says:

• sähköpostiosoitteen
• postinumeron

English naturally translates them here as the email address and the postal code.

The given word order is the most neutral and natural one:

• Tarkistan
• sähköpostiosoitteen ja postinumeron
• varmistaakseni, että tiedot ovat oikein

So it goes:

1. the main verb
2. the things being checked
3. the purpose

Finnish word order is more flexible than English word order, but changing it usually adds emphasis or changes the flow. For a standard statement, this order is very natural.