Возле нашего дома растёт липа, и в июне она приятно пахнет.

Возле means near / by / next to, and it requires the genitive case.

So:

• дом = house
• дома = of the house / near the house (genitive singular)

That is why you get:

• возле дома = near the house
• возле нашего дома = near our house

The word нашего is also in the genitive singular masculine/neuter to match дома.

Because наш has to agree with the noun in case, number, and gender.

Here the noun is дома, which is:

• masculine
• singular
• genitive

So наш changes to нашего.

Compare:

• наш дом = our house (nominative)
• возле нашего дома = near our house (genitive)

Because липа is the subject of растёт.

The sentence structure is:

• Возле нашего дома = near our house
• растёт липа = a linden tree grows / there is a linden tree growing

Even though the sentence starts with the location, липа is still the thing doing the action, so it stays in the nominative.

Because the subject is singular: липа = one linden tree.

So:

• липа растёт = the linden tree grows
• липы растут = the linden trees grow

Also note the spelling: растёт with ё. The stress is on -тёт.

Because она refers back to липа, and липа is a feminine noun in Russian.

So Russian uses the feminine pronoun:

• липа → она

In English, for a tree we usually say it, but in Russian nouns have grammatical gender, and pronouns match that gender.

Here в means in, referring to a month of time, so Russian uses the prepositional case:

• июнь = June
• в июне = in June

This is very common with months:

• в мае = in May
• в июне = in June
• в августе = in August

Because приятно here is an adverb, not an adjective.

It describes how the tree smells:

• она приятно пахнет = it smells pleasant / it smells nice

Compare:

• приятный запах = a pleasant smell
  Here приятный is an adjective describing the noun запах.
• приятно пахнет = smells pleasantly / smells nice
  Here приятно is an adverb describing the verb пахнет.

In natural English, we usually translate this as smells nice rather than smells pleasantly.

Not by itself. Пахнуть basically means to smell / to give off a smell. The smell can be good, bad, or neutral depending on context.

Examples:

• цветы пахнут приятно = the flowers smell nice
• дым пахнет плохо = the smoke smells bad
• чем пахнет? = what does it smell like? / what smell is there?

So in your sentence, the good meaning comes from приятно.

Yes, there are other possibilities.

Very similar options:

• возле нашего дома = near our house
• около нашего дома = near our house

A slightly different structure:

• рядом с нашим домом = next to / near our house

Notice the case difference:

• возле
  • genitive → возле нашего дома
• около
  • genitive → около нашего дома
• рядом с
  • instrumental → рядом с нашим домом

All are natural, but возле and около are especially close in meaning here.

Yes, that would also be correct.

Russian word order is more flexible than English. The original sentence begins with the location:

• Возле нашего дома растёт липа

This puts a little more focus on where the tree is.

You could also say:

• Липа растёт возле нашего дома

This is also grammatical and natural, but it sounds a bit more straightforward: first the subject, then the location.

So the choice is mostly about focus and style, not basic grammar.

Липа is a linden tree or lime tree in British English botanical usage.

A learner may find this confusing because English lime often makes people think of the fruit, but here it means the tree. In many contexts, linden is the clearest translation for modern learners.

So:

• липа = linden tree

Because the sentence joins two clauses:

• Возле нашего дома растёт липа
• в июне она приятно пахнет

Each part has its own predicate:

• растёт
• пахнет

In Russian, when two clauses are joined by и, a comma is often used if they are clearly separate clauses with their own grammatical structure, as here.

So the comma helps show that the sentence has two linked ideas:

1. There is a linden tree near our house.
2. In June, it smells nice.

A helpful stress guide is:

• возлЕ
• нАшего
• домА
• растЁт
• лИпа
• в июнЕ
• онА
• приятно
• пАхнет

A rough pronunciation guide:

• Возле нашего дома растёт липа, и в июне она приятно пахнет.
• VOZ-le NA-she-va da-MA ras-TYOT LEE-pa, i v ee-yu-NYE a-NA pri-YAT-na PAKH-net

A useful point: ё is always stressed, so растёт definitely has stress on that syllable.