Сачок висит у аквариума.

Here сачок means a small net, especially a hand net or fish net of the kind you might use with an aquarium.

It is a masculine noun, and in this sentence it is in the nominative singular because it is the subject.

A useful extra note: сачок can also be slang for a slacker / someone who ducks work, but that meaning is clearly not intended here.

Because the preposition у requires the genitive case.

The dictionary form is аквариум.
After у, it changes to аквариума.

So:

• аквариум = aquarium
• у аквариума = by / near the aquarium

Even though аквариум is a neuter noun, its genitive singular form is аквариума.

Here у means by, near, or next to.

So у аквариума means by the aquarium or near the aquarium.

This preposition is very common in Russian. It can also mean other things in other contexts, such as at someone's place or indicate possession, but here it is simply a location marker.

Examples of the same idea:

• у двери = by the door
• у окна = by the window
• у аквариума = by the aquarium

Not necessarily. It mainly means the net is located by / near the aquarium.

If you wanted to say it is on the aquarium, Russian would more likely use:

• на аквариуме = on the aquarium

If you wanted to say it is above the aquarium, you could say:

• над аквариумом = above the aquarium

So у аквариума is about nearness, not exact physical attachment.

Висит is the 3rd person singular present tense of висеть, which means to hang or to be hanging.

So:

• сачок висит = the net hangs / is hanging

Russian often uses one verb where English might choose between:

• hangs
• is hanging

The form висит can cover both, depending on context.

Because висит describes a state, not an action.

Compare:

• висеть = to be hanging
• вешать = to hang something up repeatedly / in process
• повесить = to hang something up once, completed

So:

• Сачок висит у аквариума. = The net is hanging by the aquarium.
• Он повесил сачок у аквариума. = He hung the net up by the aquarium.

In your sentence, the focus is on where the net is, not on who put it there.

Because in the present tense, Russian normally does not use a separate verb to be the way English does.

English says:

• The net is hanging by the aquarium.

Russian simply says:

• Сачок висит у аквариума.

This is completely normal. Russian present-tense sentences usually omit is / am / are.

Russian has no articles, so it does not have direct equivalents of a and the.

That means сачок can mean:

• a net
• the net

Which one is meant depends on context.

So Сачок висит у аквариума could be understood as either:

• A net is hanging by the aquarium
• The net is hanging by the aquarium

Usually the wider context makes it clear.

Here is the breakdown:

• сачок — masculine, nominative singular
• аквариума — genitive singular of аквариум, which is neuter

Why?

• сачок is the subject, so it is in the nominative
• у requires the genitive, so аквариум becomes аквариума

No, Russian word order is relatively flexible.

Your sentence:

• Сачок висит у аквариума.

is a natural, neutral way to say it.

But you could also say:

• У аквариума висит сачок.

This version puts more emphasis on the location first, something like By the aquarium, there is a net hanging.

The basic meaning stays the same, but the emphasis changes.

The stress is:

• сачо́к
• виси́т
• аква́риума

So the whole sentence is pronounced roughly:

• сачо́к виси́т у аква́риума

Stress is important in Russian, because it is not always predictable.

Yes. Both are possible.

• у аквариума
• около аквариума
• возле аквариума

All can mean near the aquarium.

Very roughly:

• у often feels very natural for by / right near
• около = near / around
• возле = near / next to

In many everyday situations, they are interchangeable, but у is especially common and compact.

Yes. Висит specifically suggests that the net is hanging, so it is suspended somehow.

Compare:

• сачок висит = the net is hanging
• сачок лежит = the net is lying
• сачок стоит = the net is standing

So the sentence tells you not just where the net is, but also its position.