Na het wassen laat Sofie de spinazie in het vergiet uitlekken.

This is a very common Dutch pattern:

• na = after
• het wassen = literally the washing

Here wassen is an infinitive being used like a noun. So het + infinitive often works like English -ing:

• na het eten = after eating
• voor het slapen = before sleeping
• bij het koken = while cooking / when cooking

So na het wassen means after washing.

Because Dutch normally uses het + infinitive when an infinitive is used as a noun in this kind of structure.

So:

• na het wassen = correct
• na wassen = not the normal standard form here

English can just say after washing, but Dutch usually needs the article: na het wassen.

Grammatically, na het wassen does not explicitly say who is washing. It just means after the washing / after washing.

In this sentence, most learners will naturally understand that Sofie is the one who washed the spinach, because she is the subject of the main clause. But the phrase itself does not directly state that.

If Dutch wants to make the subject completely explicit, it could say:

• Nadat Sofie de spinazie heeft gewassen, ...

That version clearly says that Sofie did the washing.

This is the verb laten plus an infinitive:

• laten can mean let, have, make, or sometimes leave in English, depending on context.

So Sofie laat de spinazie uitlekken means something like:

• Sofie lets the spinach drain
• Sofie has the spinach drain
• Sofie leaves the spinach to drain

It usually means she causes or allows the draining to happen, for example by putting the spinach in a colander and waiting.

Because after laten, Dutch uses a bare infinitive.

So you say:

• Sofie laat de spinazie uitlekken

not:

• Sofie laat de spinazie te uitlekken

This is similar to English:

• She lets it drain not
• She lets it to drain

Because uitlekken is a separable verb.

Its parts are:

• uit = out
• lekken = to leak / drain

In the dictionary form and as an infinitive, it is written as one word:

• uitlekken

But when the verb is finite in a main clause, the prefix often separates:

• De spinazie lekt uit. = The spinach drains out.

In your sentence, uitlekken is an infinitive after laat, so it stays together as one word:

• laat ... uitlekken

Because Dutch main clauses normally put the finite verb in second position, and other verbs go later, often at the end.

Here:

• Na het wassen = first element
• laat = finite verb, so it comes second
• Sofie = subject
• de spinazie = object
• in het vergiet = prepositional phrase
• uitlekken = infinitive at the end

So the structure is very typical Dutch word order.

Because spinazie is a de-word. This is something you mostly have to learn with the noun.

Also, even though spinach is an uncountable substance in English, Dutch can still use the definite article when it means a specific amount of spinach, such as the spinach being prepared here:

• de spinazie = the spinach

But in a general statement, Dutch can also leave the article out:

• Spinazie is gezond. = Spinach is healthy.

Vergiet means colander.

So:

• in het vergiet = in the colander

Dutch uses in because the spinach is placed inside the colander. That is the normal choice here.

Also note:

• het vergiet → vergiet is a het-word

So the full phrase is:

• in het vergiet

Yes. Both are natural, but they work a little differently.

• Na het wassen is shorter and more compact.
• Nadat Sofie de spinazie heeft gewassen, ... is more explicit and gives a full clause.

Compare:

• Na het wassen laat Sofie de spinazie in het vergiet uitlekken.
• Nadat Sofie de spinazie heeft gewassen, laat ze de spinazie in het vergiet uitlekken.

The first version is often preferred when the meaning is obvious and you want a concise sentence.

Yes, in natural English that is often a very good translation.

Dutch laten is flexible. In this sentence, it does not necessarily mean that Sofie is actively commanding the spinach to drain. It more naturally suggests that she puts it in the colander and allows the draining process to happen.

So depending on style, English could say:

• lets the spinach drain
• leaves the spinach to drain
• has the spinach drain

All of those reflect the Dutch reasonably well.