Právě se dívám na tu stránku a myslím, že heslo je správné.

Because the verb is dívat se, not just dívat.

In Czech, many verbs are used with se, and you have to learn them as a whole expression.
So:

• dívat se na něco = to look at / to watch something

In this sentence:

• se dívám na tu stránku = I’m looking at that page/site

The se here is not translated literally as myself. It is just part of the verb.

This is because se is a clitic, and Czech clitics usually go in the second position in the clause.

Here, Právě is the first element, so se comes right after it:

• Právě se dívám...

This sounds natural in Czech.

You may also hear:

• Dívám se právě na tu stránku.

That is possible too, but Právě se dívám... is very natural if you want to emphasize right now.

Here právě means right now, just now, or at this very moment.

So:

• Právě se dívám... = I’m looking at it right now.

Be careful: právě can also have other meanings in other contexts, such as exactly.

For example:

• Právě tak. = Exactly.

But in your sentence, it clearly means right now.

Czech does not have a separate grammatical form like the English present continuous.

So the Czech present tense can mean:

• I look
• I am looking

The context tells you which meaning is intended.

Here, právě makes it clear that the action is happening now, so:

• dívám se = I’m looking
• with právě → I’m looking right now

Because the verb dívat se na takes the accusative case.

The noun stránka is feminine, and its accusative singular form is:

• stránka → stránku

So:

• na tu stránku = at that page/site

This is a very common pattern:

• dívat se na film = to watch a film
• dívat se na televizi = to watch TV
• dívat se na stránku = to look at a page/site

Because tu is the accusative singular feminine form of ten / ta / to.

The basic forms are:

• ten = that (masculine)
• ta = that (feminine)
• to = that (neuter)

But when the feminine noun is in the accusative singular, ta changes to tu:

• ta stránka = that page/site
• vidím tu stránku = I see that page/site
• na tu stránku = at that page/site

So tu here does not mean here. It is just the correct case form of that.

It can mean either, depending on context.

stránka can mean:

• a page in a book or document
• a web page / site

In this sentence, because it also mentions heslo (password), many learners would understand it as something like:

• I’m looking at that webpage/site right now...

But the exact meaning depends on the situation.

Because Czech often omits subject pronouns when they are clear from the verb form.

The ending -ám in dívám tells you the subject is I:

• dívám = I look / I am looking
• myslím = I think

So Czech does not need já here.

You could say:

• Právě se dívám...
• Právě já se dívám...

But adding já usually gives extra emphasis, like I am the one who is looking. In a neutral sentence, it is normally left out.

A means and.

It simply connects the two clauses:

• Právě se dívám na tu stránku
• a myslím, že heslo je správné

So the sentence has the structure:

• I’m looking at that page right now, and I think that the password is correct.

Because že introduces a subordinate clause, and in Czech that is normally separated by a comma.

So:

• myslím, že... = I think that...

The comma is standard Czech punctuation.

English sometimes omits the comma before that, but Czech normally keeps it before že.

Here že means that.

So:

• myslím, že heslo je správné = I think that the password is correct

In English, that is often optional:

• I think the password is correct
• I think that the password is correct

In Czech, že is normally expressed in this kind of sentence.

For the same reason as with dívám: the verb ending already shows the subject.

• myslím = I think

So já is unnecessary unless you want emphasis or contrast:

• Já myslím, že heslo je správné, ale on nesouhlasí.
  = I think the password is correct, but he disagrees.

In your sentence, the neutral form without já is the most natural.

In this sentence, heslo most likely means password.

But heslo can also mean other things in different contexts, for example:

• slogan
• motto
• watchword

Here, because someone is looking at a page/site and evaluating whether it is correct, password is the natural meaning.

Also note that heslo is a neuter noun.

Because správné has to agree with heslo, and heslo is neuter singular.

The adjective správný changes depending on gender:

• správný = masculine
• správná = feminine
• správné = neuter

So:

• heslo je správné = the password is correct

Compare:

• kód je správný = the code is correct
• adresa je správná = the address is correct
• heslo je správné = the password is correct

It can mean both correct and right, depending on context.

So:

• heslo je správné = the password is correct
• literally also the password is right

In this context, correct is the most natural English translation.

Because dívat se means to look at / to watch, while vidět means to see.

That is an important difference:

• vidět = to see (perception)
• dívat se na = to look at / watch (intentional action)

So:

• Vidím tu stránku. = I see that page.
• Dívám se na tu stránku. = I’m looking at that page.

In your sentence, the speaker is actively examining it, so dívat se na is the right verb.

Not in exactly the same way.

• dívat se is imperfective and describes an ongoing action: to be looking / watching
• podívat se is perfective and means something like to take a look

Since the sentence says right now I’m looking, Czech uses the imperfective present:

• Právě se dívám...

If you used podívat se, it would express more of a single completed look, not an ongoing action.

Yes, it sounds natural.

A Czech speaker might also say slight variations such as:

• Právě se dívám na tu stránku a myslím si, že heslo je správné.
• Dívám se právě na tu stránku a myslím, že heslo je správné.

But your original sentence is perfectly normal and idiomatic.

One small note: some speakers like to say myslím si, while others simply say myslím. In this sentence, both are possible.