Learn Hardcore Russian: Он кидает в копилку всю мелочь, которая остаётся после магазина. - He throws all the small change that is left after the store into the piggy bank.

Кидать literally means to throw and is imperfective (ongoing / repeated / habitual action). Here it describes a regular habit: he always does this with his change.

Possible alternatives and nuances:

Он кидает в копилку… – throws it in, a bit casual, almost careless; very colloquial.
Он бросает в копилку… – also throws; a bit more neutral than кидать, still informal.
Он кладёт в копилку… – puts it in (more careful, deliberate movement).
Он опускает в копилку… – drops / inserts money in (more formal/technical, used e.g. about machines, donation boxes).

All of these are grammatically possible. The original just paints a slightly informal picture: he casually throws his change into the piggy bank each time.

Why is it в копилку and not в копилка or something else?

В can use either accusative (direction, into) or prepositional (location, in):

Direction: в копилку – into the piggy bank → accusative case
Location: в копилке – in the piggy bank → prepositional case

Here it is clearly movement into something, so we need accusative.

The noun is копилка (feminine, nominative). Feminine -а in accusative singular becomes -у:

копилка (nom.) → в копилку (acc.)

So в копилку is “into the piggy bank” and is the correct form for this meaning.

What is the base form and gender of копилку, and how would it look in other cases?

The base form is копилка – feminine noun, meaning piggy bank / money box.

Some common forms (singular):

Nominative: копилка – Это моя копилка. (This is my piggy bank.)
Accusative: копилку – Я кидаю монеты в копилку. (I throw coins into the piggy bank.)
Genitive: копилки – У меня нет копилки. (I don’t have a piggy bank.)
Prepositional: в копилке – Деньги лежат в копилке. (The money is in the piggy bank.)

Plural (just for reference):

Nominative plural: копилки – У детей есть копилки. (Children have piggy banks.)
Accusative plural: копилки (for inanimate nouns, it matches nominative) – Они купили копилки. (They bought piggy banks.)

Why is it всю мелочь and not just мелочь?

Всю мелочь = all the small change. The word всю (accusative of вся = all) emphasizes totality:

Он кидает мелочь в копилку. – He throws small change into the piggy bank.
Он кидает всю мелочь в копилку. – He throws all of the small change into the piggy bank.

So всю tells us he doesn’t keep any of the change; everything left over goes in.

Why is it всю and not весь мелочь? What gender is мелочь?

Мелочь (small change) is grammatically feminine in Russian.

That’s why:

Feminine вся / всю → вся мелочь (nom.), всю мелочь (acc.)
Masculine весь / весь → весь сахар, весь хлеб, etc.

In this sentence, всю мелочь is in the accusative (it is the direct object of кидает), so feminine вся becomes всю:

Nominative: вся мелочь остаётся… – all the change remains…
Accusative: он кидает всю мелочь… – he throws all the change…

Why do we need которая остаётся instead of just остаётся after всю мелочь?

Которая остаётся после магазина is a relative clause, like English “which is left after the store”.

Он кидает в копилку всю мелочь. – He throws all the small change into the piggy bank. (Which change?)
Он кидает в копилку всю мелочь, которая остаётся после магазина. – He throws into the piggy bank all the small change that remains after going to the store.

The clause которая остаётся после магазина specifies which мелочь we are talking about: the change left over after shopping, not just any random change.

Why is it которая, not который or которое? How does agreement work here?

The relative pronoun который / которая / которое / которые must agree with the noun it refers to in:

Gender
Number
Case

Here it refers to мелочь:

мелочь – feminine, singular, and it is the subject of the clause “remains” → nominative case.

So we choose:

Feminine singular nominative: которая

That’s why we say:

…всю мелочь, которая остаётся…
all the change that (fem. sg.) remains…

What does the reflexive verb остаётся mean here, and what is its base form?

Остаётся is 3rd person singular of оставаться (imperfective, reflexive) – to remain, to be left.

Infinitive: оставаться – to remain
Он/она: остаётся – he/she/it remains, is left

The -ся / -сь ending often makes verbs reflexive or passive-like. Here it corresponds well to English “is left”:

мелочь остаётся – the change remains / is left (over)

Perfective pair: остаться → останется (will remain, will be left):

мелочь останется – the change will remain (one-time / result).

Why do we use остаётся (imperfective present) and not the perfective future останется?

The sentence describes a regular habit and a typical situation, not a single event:

After shopping, there is (always) some change left.

In Russian, for regular, typical, or general truths in the present, we use the imperfective present:

остаётся – is (usually) left, remains (each time he goes to the store)

Perfective останется would talk about a single future result:

После магазина у него останется мелочь. – (On that specific occasion) he will have some change left.

So остаётся matches the habitual meaning of the whole sentence.

Why is it после магазина and not something like после магазин?

The preposition после (after) always takes the genitive case.

магазин (nominative) → магазина (genitive)

So we must say:

после магазина – after the store / after going to the store
Not после магазин

This is just a fixed rule: после + genitive.

Does после магазина literally mean “after the store”? How should I understand this phrase?

Literally, yes, it is “after the store” (after the shop), but idiomatically it means:

after going to the store
after he’s been to the store / after shopping

Russian often shortens such expressions:

после работы – after (finishing) work
после школы – after school (after classes)
после магазина – after (a trip to) the store

So you should understand it as after he goes shopping, not “after the shop itself does something”.

Could the word order be different, like Он всю мелочь кидает в копилку, которая остаётся после магазина?

You should not move которая остаётся после магазина away from мелочь, because it describes мелочь, not копилка.

Original:
Он кидает в копилку всю мелочь, которая остаётся после магазина.
→ The clause clearly refers to мелочь (the nearest noun).
If you say:
Он кидает в копилку, которая остаётся после магазина, всю мелочь.
it sounds like копилка “remains after the store,” which is nonsense.

Some acceptable variations (keeping the clause next to мелочь):

Он всю мелочь, которая остаётся после магазина, кидает в копилку.
Всю мелочь, которая остаётся после магазина, он кидает в копилку.

Russian word order is flexible, but the relative clause must stay close to the noun it modifies to avoid confusion.

Why is the verb кидает in the present tense? Does it mean he is doing it right now or that he does it regularly?

In this context, кидает (present, imperfective) indicates a habitual, repeated action:

Он кидает в копилку всю мелочь…
= He (always) throws all the change into the piggy bank… (each time, as a rule)

Russian often uses the present tense of an imperfective verb to describe:

routines
habits
general rules

It does not necessarily mean “right now” here; the rest of the sentence (especially после магазина) strongly suggests a regular pattern: every time he goes shopping, he does this.