После торга продавец уступил в цене.

Because после requires the genitive case.

• торг = nominative
• после торга = after bargaining / after the negotiations

So this is a standard pattern:

• после урока = after the lesson
• после работы = after work
• после торга = after bargaining

That is why you see торга.

Торг means bargaining, haggling, negotiating over price.

In this sentence, it does not mean general trade or commerce. It refers specifically to the back-and-forth discussion where buyer and seller try to agree on a price.

Useful related words:

• торг = bargaining, haggling
• торговаться = to bargain, to haggle
• торги = auction / bidding (in some contexts)

So после торга means something like after the bargaining was over.

Here уступил means gave in, made a concession, or agreed to a better price for the buyer.

The verb is уступить. It often has the idea of yielding or giving way.

In this sentence:

• продавец уступил = the seller gave in / made a concession

Because it is perfective, уступил presents the action as a completed result: the seller finally agreed to change the price.

Its imperfective partner is уступать:

• продавец уступал = the seller was yielding / used to yield / was willing to make concessions

Уступить в цене is an idiomatic expression meaning to lower the price, to come down on the price, or to give a discount after bargaining.

Literally, it is something like to уступить in price, but in natural English we would not translate it word for word.

Grammatically:

• в
  • prepositional case
• цена becomes цене

So:

• в цене = in price

But the whole phrase should be learned as one unit:

• уступить в цене = to reduce the price / to give way on price

Not exactly, though they can be similar in translation.

• уступить в цене suggests a concession, often after bargaining
• снизить цену simply means to lower the price

So:

• продавец уступил в цене = the seller came down on the price
• продавец снизил цену = the seller lowered the price

The first one sounds more tied to negotiation. The second is more neutral and does not necessarily imply bargaining.

Yes, the word order could be changed, because Russian word order is flexible.

This sentence starts with После торга to set the time/background first:

• После торга продавец уступил в цене. = After bargaining, the seller came down on the price.

You could also say:

• Продавец после торга уступил в цене.

That is also correct. The difference is mainly one of emphasis and flow, not basic meaning.

Putting После торга first makes it sound like the speaker first establishes the situation, then gives the main result.

Цене is the prepositional case singular of цена.

That is because it follows the preposition в in the fixed expression уступить в цене.

The forms are:

• цена — nominative
• цены — genitive
• цене — dative or prepositional, depending on context
• цену — accusative
• ценой / ценою — instrumental

Here it is prepositional because of в цене.

Yes, it is natural and correct Russian.

It sounds a little more neutral-written or standard than very casual conversation, but it is absolutely normal.

In everyday speech, people might also say things like:

• После торга продавец снизил цену.
• После долгих переговоров продавец уступил.
• Продавец немного скинул цену.

That last one, скинул цену, is more conversational.

So your sentence is good Russian, especially in neutral narration.

The stress is:

• После — По́сле
• торга — то́рга
• продавец — продаве́ц
• уступил — уступи́л
• в цене — в цене́

So the whole sentence is pronounced:

По́сле то́рга продаве́ц уступи́л в цене́.

For learners, the most useful thing to remember is the stress in:

• продаве́ц
• уступи́л
• цене́

Usually no, not in this meaning.

• торг = bargaining, haggling over a price
• торговля = trade, commerce, selling activity in general

So:

• после торга = after the bargaining
• после торговли would usually sound like after trading / after the selling activity, which is a different idea

If you want the idea of negotiating the price, торг is the right word here.