על הבקשה הזאת צריך לשלם אגרה קטנה, ואחר כך מקבלים אישור באימייל.

The basic meaning of על is indeed on, about, or concerning, but in Hebrew it is also very common with payments:

• לשלם על משהו = to pay for something

So על הבקשה הזאת צריך לשלם means literally something like:

• For this application/request, one has to pay

Hebrew often fronts that phrase for emphasis or topic, so the על + noun part comes first.

In normal Modern Hebrew, when you say this + noun, the noun is usually definite:

• הבקשה הזאת = this request/application
• הספר הזה = this book
• העיר הזאת = this city

So בקשה הזאת sounds incomplete or nonstandard in everyday Hebrew.

The usual pattern is:

• ה + noun + demonstrative

So:

• הבקשה הזאת
• הבקשה הזו

Both are natural.

Both mean this for a feminine singular noun.

So both of these are correct:

• הבקשה הזאת
• הבקשה הזו

The difference is mostly style and register:

• זאת is the fuller form
• זו is very common in speech and also common in writing

There is no important difference in meaning here.

This is an impersonal construction.

In Hebrew, צריך + infinitive often means:

• one has to...
• you have to...
• it is necessary to...

So:

• צריך לשלם = one must pay / you have to pay

Even though צריך is masculine singular, it is very often used as a default impersonal form in everyday Hebrew.

Other possible styles:

• אתה צריך לשלם = you have to pay, addressed to one male
• את צריכה לשלם = addressed to one female
• צריכים לשלם = people have to pay / colloquial impersonal
• יש לשלם = formal, bureaucratic, very common in official notices

לשלם is the infinitive of the verb to pay.

After words like צריך, Hebrew normally uses an infinitive:

• צריך לשלם = need to pay
• רוצה לשלם = want to pay
• אפשר לשלם = it is possible to pay

So this works just like English need to pay, where to pay follows need.

The ל at the beginning is part of the infinitive form.

Not exactly. אגרה usually means an official fee, especially a government, administrative, or processing fee.

So it is more specific than a general payment word.

Compare:

• אגרה = fee, levy, administrative fee
• תשלום = payment
• מחיר = price
• מס = tax

So אגרה קטנה suggests a small official fee, not just any amount of money.

Because in Hebrew, adjectives usually come after the noun.

So:

• אגרה קטנה = a small fee
• בית גדול = a big house
• מכונית חדשה = a new car

Also, the adjective must agree with the noun in gender and number.

Here:

• אגרה is feminine singular
• so the adjective is also feminine singular: קטנה

If the noun were definite, the adjective would also be definite:

• האגרה הקטנה = the small fee

ואחר כך means and after that, and then, or simply then.

It connects the two parts of the sentence in sequence:

1. first, the fee is paid
2. then, an approval/confirmation is received by email

Breakdown:

• ו = and
• אחר כך = afterward / later / after that

So it is a very common way to describe the next step in a process.

There is no specific they here.

Hebrew often uses third person plural as a kind of impersonal or general statement, where English might say:

• you get
• one receives
• people receive

So:

• מקבלים אישור באימייל = you receive a confirmation by email / one receives a confirmation by email

This is very common in spoken Hebrew and in practical instructions.

It does not necessarily mean that a clearly identified group of people is doing the receiving.

Because את is used before a definite direct object, not an indefinite one.

Here we have:

• אישור = a confirmation / an approval

That is indefinite, so there is no את.

Compare:

• מקבלים אישור = receive a confirmation
• מקבלים את האישור = receive the confirmation

So the absence of את matches the fact that אישור is not definite here.

Because the sentence is talking about receiving an approval/confirmation, not a previously identified specific one.

Hebrew does not have words like a or an, so the indefinite meaning is shown simply by using the noun without ה:

• אישור = a confirmation / approval
• האישור = the confirmation / approval

If the context had already introduced a specific approval, then האישור might be used.

Here ב marks the method or medium, so באימייל means:

• by email
• in an email

This use of ב is very common for means of communication or delivery.

For example:

• בטלפון = by phone / on the phone
• בדואר = by mail
• בהודעה = in a message / by message

So אישור באימייל means the confirmation comes via email.

Also, אימייל is a common modern Hebrew borrowing. A more formal alternative is דוא״ל.