Я закажу чай без сахара и буду ждать друга у окна.

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Breakdown of Я закажу чай без сахара и буду ждать друга у окна.

• я: I
• и: and
• у: by

Questions & Answers about Я закажу чай без сахара и буду ждать друга у окна.

Why is закажу used instead of заказываю or закажу буду?

Закажу is the perfective verb заказать in the simple future (1st person singular). Perfective verbs form future with a single word (закажу, закажешь, закажет...) and usually mean a completed, single action (placing an order once).
Заказываю is imperfective present and can sometimes mean a near-future plan in conversation, but here закажу is the standard, clear choice.

Why does the second verb use буду ждать instead of a one-word future like подожду?

Ждать is imperfective, so its future is made with быть + infinitive: буду ждать. This emphasizes an ongoing process (waiting for some time).
A one-word future like подожду (perfective) would sound more like wait for a while / wait a bit / finish the waiting, which can change the nuance.

Why is друга in the genitive case, not accusative?

With ждать, Russian most often uses the genitive: ждать кого? чего? → ждать друга, ждать поезда.
Accusative is possible in some contexts (often when the object is very definite/expected), but genitive is the default taught and widely used, especially in neutral sentences like this.