Kiel ajn ni ŝanĝos la skizon, arkitekto kontrolos ĝin.

Kiel ajn means however, no matter how, or in whatever way.

In this sentence, it introduces a concessive idea:
No matter how we change the sketch, an architect will check it.

A useful pattern is:

kiel ajn + clause = however / no matter how + clause

Examples:

• Kiel ajn li klarigos ĝin, mi ne kredos.
  = However he explains it, I won’t believe it.
• Kiel ajn vi faros tion, estos malfacile.
  = However you do that, it will be difficult.

Ajn adds a meaning like ever, at all, or no matter ... depending on the context.

With words like kiel, kiu, kie, kiam, it often creates an indefinite or concessive sense:

• kiu ajn = whoever / any ... whatever
• kie ajn = wherever
• kiam ajn = whenever
• kiel ajn = however / no matter how

So here, ajn is what turns plain kiel (how) into however / no matter how.

Ŝanĝos is the future tense. The ending -os always marks the future in Esperanto.

• ŝanĝas = changes / are changing
• ŝanĝos = will change

Since the main clause also has a future verb, kontrolos (will check), the sentence is talking about a future situation:

• ni ŝanĝos = we will change
• arkitekto kontrolos = an architect will check

Esperanto often keeps the tense very straightforward and explicit like this.

Because la skizon is the direct object of ŝanĝos.

In Esperanto, the ending -n marks the direct object:

• la skizo = the sketch
• la skizon = the sketch, as the thing being changed

So:

• ni ŝanĝos la skizon = we will change the sketch

This -n ending is one of the most important features of Esperanto grammar.

For the same reason: ĝin is the direct object of kontrolos.

• ĝi = it
• ĝin = it, as a direct object

So:

• arkitekto kontrolos ĝin = an architect will check it

Here ĝin refers back to la skizo / la skizon.

Because the sentence is probably talking about an architect, not the architect.

In Esperanto:

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

Esperanto has no separate word for English a/an, so an indefinite noun is usually just the bare noun:

• kuracisto venos = a doctor will come
• arkitekto kontrolos ĝin = an architect will check it

If the speaker meant a specific architect already known to the listener, then la arkitekto would be more likely.

The comma separates the subordinate clause from the main clause.

• Kiel ajn ni ŝanĝos la skizon = subordinate clause
• arkitekto kontrolos ĝin = main clause

Since the subordinate clause comes first, a comma before the main clause is normal and helpful.

This is similar to English:

• However we change the sketch, an architect will check it.

Not completely. Esperanto word order is fairly flexible because endings show the grammatical roles.

The neutral, most common order here is:

• Kiel ajn ni ŝanĝos la skizon, arkitekto kontrolos ĝin.

But other orders are possible for emphasis, for example:

• Kiel ajn ni ŝanĝos la skizon, ĝin kontrolos arkitekto.

That said, the original version is the most natural and easiest for learners.

Usually no, because kiel and kiom do different jobs.

• kiel = how, in what way, in what manner
• kiom = how much, how many, to what extent

So:

• kiel ajn ni ŝanĝos la skizon = no matter how we change the sketch
• kiom ajn ni ŝanĝos la skizon would sound odd unless you were talking about degree or amount in a very specific way

If you want to talk about manner or method, kiel ajn is the right choice.

Because skizo is a noun, and Esperanto uses ĝi as the normal third-person pronoun for things, animals, and sometimes abstractions.

So:

• la skizo = the sketch
• ĝi = it
• ĝin = it, as an object

English also uses it for things, so this part is fairly similar.

Not by itself in the strictest sense. Esperanto correlatives are forms like:

• kiel = how
• kie = where
• kiam = when
• kiu = which / who
• kio = what

These are part of the correlative system. In this sentence, kiel is the correlative element, and ajn is added to it.

So kiel ajn is a correlative-based expression meaning however / no matter how.

It has a concessive meaning: the result in the main clause stays true regardless of what happens in the first clause.

So the idea is not exactly:

• If we change the sketch...

but rather:

• No matter how we change the sketch...

That is why kiel ajn is important. It shows that the checking will happen in any case.

Yes, but it would mean something different in tone.

• ŝanĝos / kontrolos = future, more direct and real
• ŝanĝus / kontrolus = conditional, more hypothetical

So:

• Kiel ajn ni ŝanĝos la skizon, arkitekto kontrolos ĝin.
  = In the future, whatever way we change it, an architect will check it.

• Kiel ajn ni ŝanĝus la skizon, arkitekto kontrolus ĝin.
  = Hypothetically, however we might change it, an architect would check it.

Both are grammatical, but they express different levels of reality or certainty.