Mit dem Schneebesen lassen sich Eier und Milch schneller vermischen als mit einer Gabel.

Because mit always takes the dative case in German.

So:

• der Schneebesen → mit dem Schneebesen
• die Gabel → mit einer Gabel

This is why the articles change:

• der → dem
• eine → einer

A learner often notices that both phrases mean with ..., but the article endings differ because the nouns have different genders:

• Schneebesen is masculine
• Gabel is feminine

In this sentence, sich lassen + infinitive is a very common German structure meaning something like:

• can be ...
• is possible to ...
• is easy/able to be ...

So:

• Eier und Milch lassen sich schneller vermischen = Eggs and milk can be mixed together more quickly = Eggs and milk are quicker to mix together

It does not mean let themselves in a literal sense here. It is an idiomatic construction.

Because the subject is Eier und Milch, which is treated as plural.

German verbs must agree with the subject:

• das Ei lässt sich ... = the egg can be ...
• die Eier lassen sich ... = the eggs can be ...

Here the subject is:

• Eier und Milch

That combination is understood as plural, so the verb is:

• lassen

Here, sich is part of the fixed pattern sich lassen + infinitive.

It is not really reflexive in the usual English sense of themselves. Instead, it helps form this passive-like meaning:

• Das Problem lässt sich lösen. = The problem can be solved.

So in your sentence:

• Eier und Milch lassen sich vermischen = Eggs and milk can be mixed together

You should learn sich lassen + infinitive as a unit.

Because vermischen is the infinitive that goes with lassen.

In German main clauses:

• the finite verb usually comes in second position
• the second verb / infinitive often goes to the end

So the structure is:

• Mit dem Schneebesen = first element
• lassen = finite verb in second position
• sich Eier und Milch schneller = middle field
• vermischen = infinitive at the end

This is very normal German word order with two verbs.

Because German often leaves out the article when talking about things in a general way, especially with:

• plural nouns
• mass nouns
• ingredients
• substances

So:

• Eier und Milch sounds like eggs and milk in general or eggs and milk as ingredients

If you said:

• die Eier und die Milch

that would usually sound more like you mean specific eggs and specific milk already known in the context.

Both relate to mixing, but vermischen often emphasizes mixing things together into one combination.

Very roughly:

• mischen = to mix
• vermischen = to mix together / combine thoroughly

In cooking contexts, vermischen is very natural when talking about combining ingredients:

• Eier und Milch vermischen

So the sentence sounds natural and slightly more precise than plain mischen.

German usually forms the comparative of adverbs and adjectives by adding -er:

• schnell = fast / quickly
• schneller = faster / more quickly

So:

• schneller vermischen = mix together more quickly

German does not normally say mehr schnell for this meaning.

Als is used for comparisons after a comparative form like schneller.

So:

• schneller als ... = faster than ...

In the sentence:

• schneller ... als mit einer Gabel = more quickly ... than with a fork

This is the standard German pattern:

• größer als = bigger than
• besser als = better than
• schneller als = faster than

German is flexible about what comes first in a main clause. The first position is often used for whatever the speaker wants to emphasize or set as the starting point.

So beginning with:

• Mit dem Schneebesen

puts the focus on the tool: with the whisk

After that, the conjugated verb must come second:

• Mit dem Schneebesen lassen sich ...

A more neutral version could also start with the subject, for example:

• Eier und Milch lassen sich mit dem Schneebesen schneller vermischen als mit einer Gabel.

Both are grammatical, but the original highlights the whisk first.

Yes, der Schneebesen means whisk in kitchen German.

Literally, it looks like:

• Schnee = snow
• Besen = broom

But in actual usage, it simply means the kitchen utensil whisk. German compounds often look funny when translated word-for-word, so it is best to learn Schneebesen as a single vocabulary item.

Yes. German could use a passive-like idea in other ways, but sich lassen + infinitive is especially natural here.

For example, the idea is close to:

• Eier und Milch können mit dem Schneebesen schneller vermischt werden als mit einer Gabel.

That means roughly the same thing:

• Eggs and milk can be mixed more quickly with a whisk than with a fork.

However, the original sentence with lassen sich sounds smoother and more idiomatic in everyday German.