Learn Hardcore Japanese: tenin ga ryoukin to zeikin wo goukeisite kara, kurezittokaado de haraimasu. - After the clerk totals the fee and taxes, I pay by credit card.

が marks the grammatical subject of the adverbial clause here in a neutral, matter-of-fact way.
は could be used, but it would make 店員 the topic (often with a contrastive feel: “as for the clerk…”). In a simple sequence clause like 〜てから, が is more natural.
Neutral: 店員が料金と税金を合計してから…
Contrast/topic: 店員は料金と税金を合計してから… (possible, but implies contrast or that “the clerk” is already the topic in the discourse)

Who is actually paying in this sentence?

The main-clause subject is omitted and understood from context (typically “I” or “we”). The first clause’s subject is 店員 (the clerk), but the paying is done by the speaker. To make it explicit, say: 店員が料金と税金を合計してから、私はクレジットカードで払います.

Is it okay to switch subjects across 〜てから?

Yes. Japanese often omits and switches subjects across subordinate clauses. However, if there’s any chance of ambiguity, make it explicit (私は/私たちは) or use a “have someone do” form: 店員さんに合計してもらってから、クレジットカードで払います, which clearly shows the clerk does the totaling for you.

What exactly does 〜てから mean here?

〜てから means “after doing X, (then) do Y,” emphasizing strict sequence. It implies Y happens after X is completed, usually soon after. So 合計してから… means “once the totaling is done, then…”

How is 〜てから different from 〜たあと(で) and 〜たら?

〜てから: strong sense of “X first, then immediately/next Y.”
〜たあと(で): “after X (at some later time) Y.” Less emphasis on immediacy.
〜たら: “when/once/if X (is done), Y.” Can sound conditional; in practice often means “once X is done.”
Examples:
合計してから払います (first total, then pay—sequential)
合計したあとで払います (pay sometime after it’s totaled)
合計したら払います (once/if it’s totaled, I’ll pay)

Could I say 合計したら instead of 合計してから?

Yes, and it’s common. 合計したら carries a “once/when that happens” feel and can be slightly less rigid than してから. In a checkout flow, both are fine: 店員さんが合計したら、クレジットカードで払います.

Why is と used between 料金 and 税金, and why is there only one を?

と coordinately lists items exhaustively: “A and B.”
When multiple nouns share the same particle, you attach the particle once at the end: 料金と税金を (not 料金をと税金を).
If you want a non-exhaustive “A, B, etc.,” use や: 料金や税金を.

What’s the difference among 料金, 代金, 金額, 値段, 価格, 費用, and 税金?

料金: a fee/charge for a service (train fare, hotel fee).
代金: the price to be paid for goods/services (the bill/charge you owe).
金額: the monetary amount (sum of money, total).
値段: the (sticker) price of an item.
価格: price (more formal/market-level term).
費用: cost/expense (often for projects/services).
税金: tax.
In a cashier context, 代金 or 金額 is very common; 料金 also works depending on the situation.

Is 合計して natural here? Would natives say something else?

It’s fine, but you’ll also hear:

金額を計算して (calculate the amount)
合計を出して (get/produce the total)
お会計 (the check/total, as a set phrase)
Example: 合計が出てから、クレジットカードで払います or お会計が出てから、カードで払います.

Why is it クレジットカードで and not クレジットカードを?

で marks the means/method: “by/with a credit card.” Using を would wrongly treat the card as the direct object of 払う. The (implied) object is the money/bill, not the card.

Does 払います need a direct object? There isn’t one after it.

払う is transitive, but Japanese often omits obvious objects. Here, “(the amount)” is understood from context. You could say it explicitly: 料金と税金を払います or 合計金額を払います.

What’s the difference between 払います and 支払います?

支払う is a more formal/smarter register of 払う, common in written language, contracts, or polite business speech. In everyday conversation at a store, 払う is perfectly natural; in very polite speech, you might hear お支払い.

Should I add さん to 店員?

In everyday speech, 店員さん is friendlier/politer when referring to a clerk. Bare 店員 is neutral and common in descriptions or writing, but in conversation it can feel curt. So: 店員さんが合計してから… is very natural.

Why is there a comma after から?

It’s optional and used to make the pause clear for readability. Japanese commas (、) are flexible; you can include or omit them as the sentence length and rhythm suggest.

Why are there spaces between words? Japanese usually doesn’t have them, right?

Correct. The spaces are for learners. A natural write-up would be: 店員が料金と税金を合計してから、クレジットカードで払います.

How can I say this more naturally or clearly in a shop scenario?

店員さんに合計してもらってから、クレジットカードで払います. (Have the clerk total it, then pay)
合計が出てから、クレジットカードで払います. (Once the total appears)
お会計はクレジットカードでお願いします. (At checkout: “I’d like to pay by card.”)
店員さんが合計したら、カードで払います. (Once the clerk totals it…)

If I want to say “including tax,” how can I phrase it?

Use 税込み (tax-included) or 税別 (tax-excluded). For example:

税込みの金額が出てから、クレジットカードで払います.
税込みでお願いします. (when specifying how you want the total)

Is 料金と税金を合計して the best way to express “add tax to the price”?

It works, but another natural phrasing is 料金に税金を加えて (add tax to the fee) or 税金を含めて合計して (total it including tax). Cashiers often just say: 税込みで◯◯円です.

Is it okay that して is “plain” while 払います is polite?

Yes. The て-form itself isn’t plain or polite; politeness is determined by the final verb form. 〜してから、払います is standard polite style.