Learn Hardcore Russian: Моё лицо может покраснеть на солнце.

Because лицо is a neuter noun, not masculine.
Russian possessive adjectives agree with the gender (and number, case) of the noun they modify:

masculine: мой стол (my table)
feminine: моя рука (my hand)
neuter: моё лицо (my face)
plural: мои руки (my hands)

So with лицо (neuter), you must use моё.

What case is моё лицо, and what is its role in the sentence?

Моё лицо is in the nominative case.
It is the subject of the sentence – the thing that can become red.
The structure is:

subject: моё лицо
verb phrase: может покраснеть
adverbial phrase: на солнце

Why is the verb может in 3rd person singular?

Because the subject is лицо, which is 3rd person singular (like it in English).
The verb мочь (to be able to, can) conjugates as:

я могу
ты можешь
он/она/оно может
мы можем
вы можете
они могут

Here we have оно (лицо) → может.

Why is the main verb покраснеть and not краснеть?

Both exist, but the aspect is different:

краснеть – imperfective: to be red / to turn red as a process or repeated tendency.
покраснеть – perfective: to become red, to go red (focus on the result / change).

In может покраснеть, the speaker talks about the possible change from normal color to red in the sun.
If you said может краснеть, it would sound more like is able to be red or tends to be red rather than might go red.

Why is there an infinitive (покраснеть) after может?

In Russian, modal verbs like мочь (can, to be able to) are normally followed by the infinitive of the main verb:

Он может читать. – He can read.
Я могу помочь. – I can help.
Моё лицо может покраснеть. – My face can go red.

So может + покраснеть is the standard modal construction.

What is the tense and time meaning of может покраснеть?

Grammatically, может is in present tense, and покраснеть is infinitive (perfective).
But because the infinitive is perfective, the whole phrase refers to a possible future result:

literally: My face *can (now / in general) become red in the sun (in the future / whenever I’m in the sun).*

So structurally it’s “present + infinitive,” but semantically it describes what may happen.

What does на солнце literally mean, and why isn’t it “on the sun”?

Literally, на солнце is “on the sun”, but in Russian this phrase is used idiomatically to mean:

in the sun / in the sunlight / when exposed to the sun

So:

сидеть на солнце – to sit in the sun
сохнуть на солнце – to dry in the sun
Моё лицо может покраснеть на солнце. – My face can go red in the sun.

It uses на + prepositional case (солнце) here.

Why is it на солнце and not от солнца?

Both are possible, but they emphasize slightly different things:

на солнце – in the sun, while you are in direct sunlight (a condition / place)
- Focus: the situation of being in the sun.
от солнца – from the sun, because of the sun (a cause)
- Focus: the sun as the cause.

So:

Моё лицо может покраснеть на солнце. – When I’m in the sun, my face may go red.
Моё лицо краснеет от солнца. – My face goes red because of the sun.

Could I say Моё лицо краснеет на солнце instead? How would it differ?

Yes, that’s also correct, but the nuance changes:

Моё лицо может покраснеть на солнце.
→ It can go red / it might go red in the sun (possibility, potential).
Моё лицо краснеет на солнце.
→ It does go red in the sun, as a regular fact / tendency.

The original sentence stresses possibility; краснеет states it as something that actually happens (usually).

Is the word order flexible? Can I say На солнце моё лицо может покраснеть?

Yes, Russian word order is fairly flexible. These are all grammatical:

Моё лицо может покраснеть на солнце.
На солнце моё лицо может покраснеть.
Моё лицо на солнце может покраснеть.

The default neutral order is usually subject–verb–other elements, like the original.
Putting на солнце first (На солнце моё лицо…) slightly emphasizes the condition “in the sun”.

How do you pronounce солнце and where is the stress?

Stress: сОлнце – stress on the first syllable.
Pronunciation: the л is not clearly pronounced, so it sounds roughly like [сóн-це].

So the whole sentence is stressed:

моЁ лицО мОжет покраснЕть на сОлнце

Are there other verbs I could use if I mean “get sunburnt” rather than just “go red”?

Yes, if you want to stress sunburn, you would normally use:

обгореть на солнце – to get sunburnt in the sun
- Моё лицо может обгореть на солнце. – My face can get sunburnt in the sun.

Покраснеть just describes becoming red, which could be from sun, embarrassment, alcohol, etc., without necessarily implying serious sunburn.