У кассы я разменяю купюру и заплачу мелкими монетами.

У basically means “by/near/at (someone/something)” and it requires the genitive case.
So у кассы literally means “by the register/cash desk.”

• Nominative: касса
• Genitive: кассы (after у)

Yes, but the meaning shifts:

• у кассы = near/at the register (physically next to it); very common for “at the checkout.”
• на кассе = at the register as a workstation (often implies someone is working there): Она работает на кассе.
• в кассе = in the cash desk / in the cash register (inside it), or “in the cashier’s office” depending on context; not what you want for “at checkout.”

For a customer standing at checkout, у кассы is the most natural.

Russian uses present forms as future only with imperfective verbs. Here the verbs are perfective, so their “present-looking” forms actually mean simple future:

• разменяю (perfective) = I will break / exchange (once, as a completed action)
• заплачу (perfective) = I will pay (once, completed)

If you used imperfective, you’d get:

• я разменяю (PF) = I’ll break it (one time, result-focused)
• я разменю is not standard; the normal PF is разменять → разменяю
• я размениваю (IPF) = I’m breaking / I break (process/habit), not a future by itself

• разменяю (perfective, from разменять) focuses on the result: you end up with change.
• размениваю (imperfective, from разменивать) focuses on the process or a repeated action.

In this sentence, you’re describing a planned, one-time action with a clear result, so разменяю fits best.

Because разменять takes a direct object: you “break/exchange” something.
купюра (banknote) is feminine, so accusative singular is купюру:

• купюра (nom.) → купюру (acc.)

разменять купюру means to break a bill (get smaller denominations/coins for it).
It’s not primarily “exchange currency” (like dollars to euros). For currency exchange you’d more likely use:

• обменять деньги = exchange money (often between currencies)
• обменять доллары на рубли = exchange dollars for rubles

Here the idea is: “I’ll break a banknote into smaller money.”

мелкими монетами is instrumental plural, used to express the means/instrument: “pay with something.”

• монеты (nom. pl.) → монетами (instr. pl.)
• мелкие (nom. pl.) → мелкими (instr. pl., agreeing with монетами)

So it literally means “I will pay by means of small coins.”

Yes:

• заплачу мелкими монетами = I’ll pay with small coins (explicit, a bit more “countable/physical”).
• заплачу мелочью = I’ll pay with change / small cash (more general, very natural colloquially).

мелочь can include coins and sometimes small-denomination bills depending on context, but it usually implies “small change.”

You can omit я if the subject is clear:

• У кассы разменяю купюру и заплачу мелкими монетами. (sounds fine)

Including я can add emphasis/contrast (“I will…” as opposed to someone else) or just reflect a more explicit style.

Russian word order is flexible and often reflects emphasis. This version is neutral and clear:

• У кассы (sets the scene)
• я (subject)
• разменяю купюру (first action)
• и заплачу мелкими монетами (second action)

Other natural варианты:

• Я у кассы разменяю купюру и заплачу мелкими монетами. (slightly more focus on “I”)
• У кассы я заплачу мелкими монетами, разменяв купюру. (more “literary,” using a participle)

заплатить can be used without a direct object when it’s obvious you mean “pay (the bill/for the purchase).”
If you want to specify what you pay for, Russian often uses за + accusative:

• заплачу за покупку = I’ll pay for the purchase
• заплачу за билет = I’ll pay for the ticket

But in a checkout context, заплачу alone is completely normal.

Common stresses:

• у кассы: КА́ссы
• разменя́ю (stress on -я́-)
• купю́ру (stress on -ю́-)
• заплачу́ (stress on the last syllable)
• ме́лкими (stress on ме́л-)
• моне́тами (stress on -не́-)