Learn Hardcore Polish: Czasem prawda boli bardziej niż małe kłamstwo. - Sometimes the truth hurts more than a small lie.

They are basically stylistic variants; there is no real difference in meaning.
Czasem is slightly shorter and a bit more common in everyday speech and writing.
You can safely treat them as interchangeable in sentences like this:
- Czasem prawda boli bardziej niż małe kłamstwo.
- Czasami prawda boli bardziej niż małe kłamstwo.

Both sound natural.

Can czasem go in a different place in the sentence?

Yes. Polish word order is quite flexible, and adverbs of time (like czasem) can move around without changing the basic meaning. All of these are possible:

Czasem prawda boli bardziej niż małe kłamstwo.
Prawda czasem boli bardziej niż małe kłamstwo.
Prawda boli czasem bardziej niż małe kłamstwo.

Differences are mostly about rhythm and slight emphasis:

Putting czasem first (Czasem prawda…) makes sometimes the starting point of the thought.
Putting czasem after prawda (Prawda czasem boli…) slightly emphasizes truth first, then tells you that sometimes it hurts.

All are natural; the original version is very typical.

Why is there no the or a before prawda and małe kłamstwo?

Polish does not use articles (no a, an, the), so:

prawda can mean the truth, truth, or a truth, depending on context.
małe kłamstwo can mean a small lie or the small lie.

Definiteness is understood from context or can be clarified with other words if needed, e.g.:

ta prawda – this / that truth
to małe kłamstwo – this / that small lie

But in a general proverb-like sentence like this, bare nouns without articles are normal and expected in Polish.

What is the grammatical role and form of prawda here?

Prawda (truth) is:

a feminine noun,
in the nominative singular form,
functioning as the subject of the verb boli.

So the basic structure is:

prawda (subject) + boli (verb) → the truth hurts.

You could expand it to a more explicit version:

Czasem to prawda boli bardziej niż małe kłamstwo.
(Sometimes it is the truth that hurts more than a small lie.)

But the simple Prawda boli is already a complete subject–verb pair.

What exactly is boli? Why not something like jest bolesna?

Boli is the 3rd person singular form of the verb boleć – to hurt / to ache.

(coś) boli = (something) hurts
- Głowa boli. – The head hurts / I have a headache.
- Prawda boli. – The truth hurts.

Jest bolesna uses an adjective bolesna (painful):

Prawda jest bolesna. – The truth is painful.

Both are grammatically correct, but they differ slightly:

Prawda boli – focuses on the act of causing pain (hurting).
Prawda jest bolesna – describes the quality (being painful).

In the proverb-like sentence, Prawda boli is more direct and idiomatic.

Why is it małe kłamstwo and not mała kłamstwo?

Because kłamstwo (lie) is a neuter noun, and the adjective must agree with it in gender, number, and case.

kłamstwo – neuter noun, nominative singular
the matching adjective form is małe – neuter, nominative singular

So:

małe kłamstwo – a small lie (correct)
mała kłamstwo – incorrect (because mała is feminine)

Other examples of agreement:

duże kłamstwo – a big lie
niewinne kłamstwo – an innocent lie

What case is małe kłamstwo in, and what is its function?

Małe kłamstwo is in the nominative singular:

małe – nominative, neuter, singular
kłamstwo – nominative, neuter, singular

Functionally, it is the (implied) subject of the verb boli in the second, omitted part of the comparison:

Czasem prawda boli bardziej niż małe kłamstwo (boli).
(Sometimes the truth hurts more than a small lie (hurts).)

Polish very often omits repeated verbs in comparative clauses when the meaning is clear.

Why is there no verb after niż małe kłamstwo? Is that normal?

Yes, it is completely normal and very common.

The full, explicit version would be:

Czasem prawda boli bardziej niż małe kłamstwo boli.

But Polish usually drops the repeated verb in comparisons to avoid redundancy, just like English often does:

English: It hurts more than a small lie (does).
Polish: …bardziej niż małe kłamstwo (boli).

The verb boli is understood from the first part, so repeating it is unnecessary unless you want extra emphasis or absolute clarity in a tricky sentence.

What does bardziej modify here: the verb boli or something else?

Here bardziej is an adverb modifying the verb boli:

boli bardziej – hurts more

So the structure is:

prawda – subject
boli bardziej – verb + degree adverb
niż małe kłamstwo – comparative phrase (than a small lie)

You could rephrase it (keeping the same meaning) as:

Czasem prawda bardziej boli niż małe kłamstwo.

Both boli bardziej and bardziej boli are acceptable, with only a slight difference in emphasis.

Could we use od instead of niż in this comparison?

In this particular sentence, niż is the natural choice:

Czasem prawda boli bardziej niż małe kłamstwo. ✅

Niż is the standard word used in full comparative clauses, especially when you have (or can have) a verb in the second part:

Jest wyższy niż ja. – He is taller than I am.
Boli bardziej niż myślałem. – It hurts more than I thought.

Od is often used with comparative adjectives/adverbs without a full clause:

Prawda bywa bardziej bolesna od kłamstwa. – The truth can be more painful than a lie.
On jest starszy od niej. – He is older than her.

You could say something like:

Prawda czasem boli mocniej od małego kłamstwa.

but that slightly changes the structure and wording. For the given sentence, niż is the most idiomatic.

Is małe kłamstwo singular or could it mean small lies in general?

Grammatically, małe kłamstwo is singular:

kłamstwo – one lie
małe kłamstwa – small lies (plural)

However, in a proverb-like, general statement, a small lie can be understood conceptually as the kind of small lie, not one specific instance. So:

małe kłamstwo here = a small lie in general, as a type.

If you really wanted to stress plurality, you could say:

Czasem prawda boli bardziej niż małe kłamstwa.
(Sometimes the truth hurts more than small lies.)

Is małe kłamstwo exactly the same as white lie in English?

Not exactly, though they often overlap.

małe kłamstwo literally: a small lie
white lie in English: a socially acceptable, harmless lie, usually told not to hurt someone.

Polish equivalents for white lie could be:

niewinne kłamstwo – innocent lie
drobne kłamstwo – minor / small lie (very close in feel)

In many contexts, małe kłamstwo can function like a small / white lie, but it does not automatically include the nuance of being socially acceptable or harmless; that can depend on context.

How would you negate this idea in Polish, e.g. Sometimes the truth doesn’t hurt as much as a small lie?

A natural negated version would be:

Czasem prawda nie boli tak bardzo jak małe kłamstwo.
Sometimes the truth doesn’t hurt as much as a small lie.

Key points:

nie boli – negation of boli
tak bardzo jak – as much as (for intensity)
The structure is parallel to the original:
- (prawda) nie boli tak bardzo jak (małe kłamstwo (boli)).

Again, the verb after the second part is understood and omitted.