Подрезка осталась точной, даром что нижнее вращение было слабым.

In this sentence, подрезка is a sports term, especially natural in table tennis. It refers to a chop / underspin shot or the act of playing that kind of stroke.

Outside sports, подрезка can also mean trimming, cutting back, or pruning, so context matters. Here, because of нижнее вращение (spin), the sports meaning is the one to use.

Because подрезка is a feminine singular noun, and the past-tense verb agrees with it.

• подрезка — feminine singular
• осталась — feminine singular past form of остаться

Compare:

• удар остался точным — masculine
• подача осталась точной — feminine
• вращение осталось слабым — neuter

Осталась is the perfective past form of остаться. It presents the result: the shot remained precise, despite the weak spin.

This is different from оставалась, the imperfective form, which would sound more like an ongoing background description:

• подрезка оставалась точной — it kept being precise / was staying precise

Here, осталась is more natural because the sentence points to a completed situation and its outcome.

Because after verbs like остаться, Russian often uses the instrumental case for the predicate adjective.

So:

• точная — nominative
• точной — instrumental feminine singular

That is why you get:

• Подрезка осталась точной

This pattern is very common with verbs such as:

• быть
• стать
• оказаться
• остаться

For example:

• Она стала спокойной
• Он остался довольным
• Игра оказалась трудной

Даром что is a fixed expression meaning even though, although, or despite the fact that.

So:

• Подрезка осталась точной, даром что нижнее вращение было слабым means:
• the chop remained precise, even though the underspin was weak

It introduces a concession: one fact is true in spite of another fact.

Yes historically, but in this sentence you should treat даром что as a single fixed conjunction.

On its own, даром can mean:

• for nothing
• for free
• sometimes in vain

But даром что does not mean anything like for free that. As a whole expression, it simply means although / even though.

So it is best learned as one chunk:

• даром что = even though

Because даром что introduces a subordinate clause.

Main clause:

• Подрезка осталась точной

Subordinate concessive clause:

• даром что нижнее вращение было слабым

Russian normally separates this kind of clause with a comma, just as English often separates although clauses.

Literally, it is lower spin or bottom spin, but in sports English the normal term is usually backspin or underspin.

So нижнее вращение is the type of spin where the ball rotates in a way that produces underspin.

Word by word:

• нижнее — lower, bottom
• вращение — rotation, spin

In table tennis language, this is a standard technical phrase.

Because вращение is a neuter singular noun.

So the past-tense form of быть agrees with it:

• masculine: был
• feminine: была
• neuter: было
• plural: были

Since нижнее вращение is neuter singular, the sentence uses:

• нижнее вращение было...

For the same reason that точной is instrumental: after быть in the past tense, Russian very often uses the instrumental case in the predicate.

So:

• слабое — nominative neuter singular
• слабым — instrumental singular

That gives:

• нижнее вращение было слабым

This is a very standard structure in Russian.

Была точной simply says that it was precise.

Осталась точной adds the idea that it continued to be precise or still ended up being precise, despite some possible reason for it not to be.

That makes it a very good match with даром что:

• the shot remained precise,
• even though the spin was weak

So осталась creates a stronger sense of contrast and resilience than plain была.

Yes. Russian word order is fairly flexible, and changing it mostly affects emphasis.

For example:

• Даром что нижнее вращение было слабым, подрезка осталась точной.

This version puts the concessive idea first: even though the underspin was weak...

The original order is also very natural:

• Подрезка осталась точной, даром что нижнее вращение было слабым.

That version states the result first, then adds the contrasting detail.