Learn Russian: Пожалуйста, позвоните заказчику насчёт сметы. - Please call the client regarding the estimate.

Both can be translated as 'about', but насчёт has a slightly more formal, business-like tone, much like 'regarding' or 'concerning' in English. Grammatically, насчёт always takes the Genitive case (which is why we see сметы here), whereas о requires the Prepositional case (о смете).

Could насчёт be written as two separate words (на счёт) here?

No, it must be written as a single word when used as a preposition meaning 'regarding'. If written as two words (на счёт), it is a combination of the preposition на and the noun счёт (account or bill), meaning literally 'onto the account', such as when transferring money to a bank account.

Why is the word for client written as заказчику instead of заказчика?

In Russian, the verb позвонить (to call by phone) always requires the target of the call to be in the Dative case, as you are directing your action 'to' them. Therefore, the masculine noun заказчик takes the Dative ending -у.

What type of estimate does смета refer to?

In a business or construction context, смета refers to a formal, itemized cost estimate or budget document. It is not a mental guess or rough approximation, which would be better translated by a word like оценка.