Снегоступы и гамаши лежат здесь.

They are in the nominative plural.

In this sentence, снегоступы и гамаши are the subject: they are the things that are lying here. Subjects are normally in the nominative case in Russian.

• снегоступ → снегоступы
• гамаша → гамаши (though this word is very often used in the plural)

Because the subject is plural: снегоступы и гамаши = snowshoes and gaiters.

Лежат is the 3rd person plural form of лежать.

A quick comparison:

• лежит = is lying / lies for one thing
• лежат = are lying / lie for more than one thing

Since there are two items joined by и (and), Russian uses the plural verb.

Russian often prefers a more specific verb where English just uses to be.

лежать literally means to lie or to be lying. It is commonly used for things that are resting somewhere, especially not upright.

So:

• Снегоступы и гамаши лежат здесь. = The snowshoes and gaiters are lying here / are here

In natural English, we might just say are here, but Russian often chooses a position verb such as:

• лежать = to lie
• стоять = to stand
• висеть = to hang

Because лежать suggests that the items are resting in a lying position, not standing upright.

For objects, Russian often distinguishes their position:

• лежать = to lie, be lying
• стоять = to stand, be standing
• висеть = to hang, be hanging

Snowshoes and gaiters are naturally thought of as things laid down somewhere, so лежат sounds normal.

If you said стоят, it would suggest they are somehow positioned upright, which would sound odd in most contexts.

Yes, Russian word order is fairly flexible.

Снегоступы и гамаши лежат здесь is a normal order, with the location placed at the end.

You could also say:

• Здесь лежат снегоступы и гамаши.
• Снегоступы и гамаши здесь лежат. (more marked, depending on emphasis)

The difference is mainly about focus and emphasis, not basic grammar.

• Снегоступы и гамаши лежат здесь = neutral statement
• Здесь лежат снегоступы и гамаши = stronger focus on here

Yes, but they behave a little differently.

• снегоступ = snowshoe
• снегоступы = snowshoes

For гамаши, the singular гамаша exists, but in real usage the plural гамаши is much more common, similar to how some clothing items are often talked about as a pair.

So a learner will most often meet:

• гамаши = gaiters / leggings

Because both items are naturally thought of as paired objects.

Just as English says:

• snowshoes
• gaiters

Russian also commonly uses the plural:

• снегоступы
• гамаши

So the sentence could easily mean one pair of snowshoes and one pair of gaiters are here.

Because Russian has no articles.

Russian does not have direct equivalents of English a/an and the. Whether something is definite or indefinite is usually understood from context.

So Снегоступы и гамаши лежат здесь could mean:

• The snowshoes and gaiters are here
• Snowshoes and gaiters are here

The context tells you which interpretation is intended.

The stress is:

снегосту́пы и гама́ши лежа́т здесь

A rough English-friendly guide:

snyi-ga-STOO-py i ga-MA-shi lyi-ZHAT zdyes

A few useful notes:

• ж sounds like the s in measure
• ы is a Russian vowel with no exact English equivalent
• здесь is one syllable, roughly zdyes

It can do both.

In this sentence, лежат often describes a state rather than an active event. It means that the snowshoes and gaiters are currently there, in a lying position.

So depending on context, English could translate it as:

• are lying here
• are here

Russian present tense often covers both the idea of current state and present situation.

Yes. In many contexts, здесь and тут both mean here.

So you could say:

• Снегоступы и гамаши лежат здесь.
• Снегоступы и гамаши лежат тут.

The difference is small. Very broadly:

• здесь = slightly more neutral
• тут = often a bit more conversational

In everyday speech, both are very common.