Se via stomako doloras, ne manĝu tro rapide.

Se means if. It introduces a condition:

• Se via stomako doloras = If your stomach hurts

This is very straightforward in Esperanto: se + clause, just like English if + clause.

Because vi means you, but via means your.

In Esperanto, many possessive words are formed by adding -a:

• mi = I → mia = my
• vi = you → via = your
• li = he → lia = his

So:

• via stomako = your stomach

In Esperanto, nouns end in -o.

So:

• stomako = stomach
• hundo = dog
• domo = house

That -o is just the normal noun ending.
Here, stomako is the noun that acts as the subject of doloras.

The ending -as marks the present tense in Esperanto.

So:

• doloras = hurts / is hurting

The verb is dolori = to hurt, to ache.
In this sentence:

• via stomako doloras = your stomach hurts

Esperanto uses -as for present tense no matter who or what the subject is.

Because Esperanto verbs do not change according to person.

In English, we say:

• I eat
• you eat
• he eats

In Esperanto, the verb form stays the same:

• mi manĝas
• vi manĝas
• li manĝas

In via stomako doloras, the subject is actually stomako (stomach), not via. But even if the subject were different, the present-tense ending would still be -as.

Because manĝu is the command / request / instruction form.

Esperanto uses -u for this mood:

• Manĝu! = Eat!
• Ne manĝu! = Don’t eat!

So:

• ne manĝu tro rapide = don’t eat too quickly

If you said ne manĝas, that would mean is not eating / does not eat, which is a statement, not a command.

Yes. Just like English eat, Esperanto manĝi can be used without a direct object when the object is general or obvious.

So:

• Mi manĝas. = I’m eating.
• Ne manĝu tro rapide. = Don’t eat too quickly.

You do not need to mention food explicitly.

Because rapide is an adverb, and adverbs modify verbs.

• rapida = fast, quick (adjective)
• rapide = quickly (adverb)

Here it modifies manĝu:

• manĝu rapide = eat quickly

Since it describes how someone should eat, the adverb form -e is required.

Tro means too in the sense of excessively.

So:

• tro rapide = too quickly

A few related words:

• tre rapide = very quickly
• tro rapide = too quickly

That difference is important:

• tre = very
• tro = too much / excessively

The comma separates the if-clause from the main clause:

• Se via stomako doloras, ne manĝu tro rapide.

This is also common in English:

• If your stomach hurts, don’t eat too quickly.

The comma helps readability. In Esperanto, it is very normal to put a comma after an introductory conditional clause like this.

Yes, to some extent. Esperanto word order is fairly flexible, though the most neutral version here is:

• Se via stomako doloras, ne manĝu tro rapide.

You could also say:

• Ne manĝu tro rapide, se via stomako doloras.

That still makes sense. The original version feels natural because it gives the condition first and then the advice.