Ni aĉetos kahelojn, kondiĉe ke arkitekto elektos ilin.

Because kahelojn is a plural direct object.

• -j marks the plural: kaheloj = tiles
• -n marks the direct object: the thing being bought

So:

• Ni aĉetos kahelojn = We will buy tiles

In Esperanto, direct objects usually take -n, even when English does not show any special ending.

For the same reason: ilin is a direct object pronoun.

• ili = they
• ilin = them as an object

In arkitekto elektos ilin, the architect is choosing them, so the pronoun needs -n.

Also, ilin is plural because it refers back to kahelojn.

Because both actions are understood as happening in the future.

• Ni aĉetos = we will buy
• arkitekto elektos = an architect will choose

Esperanto normally uses its tenses quite straightforwardly. If something is future from the speaker’s point of view, -os is natural.

So the sentence means something like:

• We will buy the tiles, provided that an architect chooses them.

Because this sentence is stating a condition, not giving a command or expressing a wish.

• elektos = will choose
• elektu = choose / let ... choose / should choose in a command-like or volitional sense

After kondiĉe ke, Esperanto often uses an ordinary tense form, as here. The speaker is not telling the architect to choose; the speaker is saying that the purchase will happen on that condition.

So elektos is the normal choice here.

Kondiĉe ke means provided that, on condition that, or as long as.

It introduces a condition that must be satisfied.

So:

• Ni aĉetos kahelojn, kondiĉe ke arkitekto elektos ilin.
• We will buy tiles, provided that an architect chooses them.

It is a bit more specific and formal than plain se (if).

Sometimes yes, but the nuance is a little different.

• se = if
• kondiĉe ke = provided that / on condition that

Se can sound like a general possibility:

• Ni aĉetos kahelojn, se arkitekto elektos ilin.

Kondiĉe ke stresses that this is a requirement or condition:

• We’ll buy the tiles only on that condition.

So kondiĉe ke is a good choice when you want the condition to sound explicit.

Because Esperanto has no indefinite article.

English distinguishes:

• an architect
• the architect

Esperanto only has the definite article la. If there is no la, the noun can often mean an architect or just architect depending on context.

So:

• arkitekto = an architect / architect
• la arkitekto = the architect

That depends on the context.

Use la arkitekto if you mean a specific architect already known to the listener:

• the architect

Use just arkitekto if the person is not being identified specifically, or if English would say an architect.

So this sentence suggests:

• provided that an architect chooses them

If you meant a particular architect, you would probably say:

• kondiĉe ke la arkitekto elektos ilin

The basic word order is natural, but Esperanto is fairly flexible because the endings show the grammar.

This sentence follows a very common pattern:

• Ni aĉetos kahelojn = main clause
• kondiĉe ke arkitekto elektos ilin = subordinate clause

Because kahelojn and ilin clearly mark the objects, the meaning stays clear even if the order changes somewhat. Still, the given order is the most straightforward and natural for learners.