Im Sommer gibt es am See viele Mücken.

Es gibt is the standard German way to say there is or there are.

So:

• Es gibt viele Mücken. = There are many mosquitoes.

German usually does not use ist/sind the way English uses there is/there are.
A sentence like Viele Mücken sind am See would mean something more like Many mosquitoes are at the lake, which is possible, but it focuses more on the mosquitoes as the subject rather than simply stating that they exist there.

In your sentence, gibt es is the natural choice for introducing the presence of something.

Both are possible.

German often moves a time phrase or place phrase to the beginning of the sentence for emphasis or to set the scene.

• Im Sommer gibt es am See viele Mücken. = In summer, there are many mosquitoes at the lake.
• Es gibt im Sommer am See viele Mücken. = also correct, but slightly less natural in many contexts

When something other than the subject comes first in German, the verb still stays in second position. That is why you get:

• Im Sommer
  • gibt
    • es ...

This is a very important German word-order rule: the finite verb is usually in position 2 in main clauses.

Im is a contraction of:

• in dem → im

German often uses the definite article with seasons, so im Sommer literally means in the summer, though in English we often just say in summer.

Common examples:

• im Sommer = in summer
• im Winter = in winter
• im Frühling = in spring
• im Herbst = in autumn/fall

So in Sommer by itself is not correct here.

Because this sentence describes a location, not movement.

• am See = an dem See = at/by the lake
• an den See = to the lake

German uses different cases after certain prepositions depending on whether you mean:

• location → dative
• direction/movement toward somewhere → accusative

With an:

• am See = at the lake / by the lake (dative, location)
• an den See = to the lake (accusative, direction)

Here, the mosquitoes are located there, so am See is correct.

Because German often uses no article with plural nouns when speaking about an indefinite quantity.

• viele Mücken = many mosquitoes

You are not talking about specific mosquitoes already known to the listener, so there is no need for die.

Compare:

• viele Mücken = many mosquitoes
• die Mücken = the mosquitoes
• die vielen Mücken = the many mosquitoes

So in this sentence, viele Mücken is the natural indefinite plural phrase.

It is in the accusative case.

A key rule is:

• es gibt always takes the accusative

So:

• es gibt einen See
• es gibt viele Mücken
• es gibt ein Problem

With viele Mücken, you do not see a special plural accusative ending here, but grammatically it is still accusative.

In es gibt, the es is part of the fixed expression meaning there is/there are. It usually does not translate as normal English it.

So it is better to learn es gibt as one unit:

• es gibt = there is / there are

For example:

• Es gibt ein Hotel hier. = There is a hotel here.
• Es gibt viele Mücken. = There are many mosquitoes.

Because they are nouns, and in German all nouns are capitalized.

• der Sommer
• der See
• die Mücke / die Mücken

This is one of the most noticeable spelling differences between English and German.

The singular is:

• die Mücke = the mosquito

The plural is:

• die Mücken = the mosquitoes

The ü is an umlauted vowel. It is pronounced differently from u. If you cannot type ü, you can write:

• Muecke
• Muecken

That is the standard replacement in German spelling when umlauts are unavailable.

Yes, that is grammatically possible, but it sounds more marked or emphatic.

German allows different word orders depending on what you want to emphasize. For example:

• Im Sommer gibt es am See viele Mücken.
  Neutral, natural: sets the time first.

• Am See gibt es im Sommer viele Mücken.
  Emphasizes the place.

• Viele Mücken gibt es am See im Sommer.
  Emphasizes many mosquitoes; this sounds more stylistically marked.

So your original sentence is a very natural everyday version.

Usually at the lake or by the lake.

• am See literally comes from an dem See
• with places like this, English translation depends on context

Most likely meanings:

• at the lake
• by the lake

On the lake would usually suggest being physically on the water, which German would express differently depending on the exact meaning.

So for this sentence, at the lake or by the lake is the best match.

It can mean both, depending on context.

• im Sommer can refer to in summer generally
• or in the summer in a specific situation

In this sentence, it most naturally means something general, like:

• In summer, there are many mosquitoes at the lake.

So even though German uses the article (dem → im), English may or may not use the in translation.