Если Вы любите тихие места, Вам понравятся этот сквер и длинная аллея.

Вы can mean either:

• you (plural), or
• you addressed politely to one person

In both cases, Russian uses the plural verb form, so Вы любите is correct.

The capital letter in Вы is a politeness convention in writing when addressing one person respectfully. In many modern texts, you may also see lowercase вы.

Тихие места is in the accusative plural, because it is the direct object of любите.

The important point is that места is inanimate. In Russian, for inanimate plural nouns, the accusative looks the same as the nominative:

• nominative: тихие места
• accusative: тихие места

So the adjective stays тихие, not тихих.

Compare that with an animate plural object:

• Я люблю хороших людей
  Here людей is animate, so the accusative matches the genitive.

This is because нравиться / понравиться works differently from English to like.

In Russian, the thing that is liked becomes the subject, and the person who likes it is put in the dative case:

• Мне нравится книга = I like the book
• literally: The book is pleasing to me

So:

• Вам понравятся этот сквер и длинная аллея

literally means something like:

• This small park and long alley will be pleasing to you

That is why you get Вам, not Вы.

Because the grammatical subject is two things together:

• этот сквер
• длинная аллея

Together they form a plural subject, so the verb must also be plural:

• Вам понравятся этот сквер и длинная аллея

If there were only one thing, you would use singular:

• Вам понравится этот сквер
• Вам понравится длинная аллея

These are different aspects of the same verb:

• нравиться = imperfective
• понравиться = perfective

In this sentence, понравятся is the future form of the perfective verb, and it means something like:

• you will like
• you will come to like
• you will find pleasing

This is natural when talking about someone’s reaction after seeing or experiencing something.

Compare:

• Мне нравятся тихие места = I like quiet places in general
• Мне понравится этот сквер = I will like this small park

Russian often uses the present tense after если for a general or real condition:

• Если Вы любите тихие места... = If you like quiet places...

This is very similar to English, which also says If you like..., not usually If you will like...

A future form here would sound unnatural unless you really meant a future change in preference.

As written, этот modifies only сквер:

• этот сквер = this small park / this square

But длинная аллея has no demonstrative. It simply means a long alley or the long alley, depending on context, because Russian has no articles.

If you want to say this long alley, then you should say:

• эта длинная аллея

So yes: этот cannot also cover аллея, because the forms must agree in gender:

• этот сквер — masculine
• эта аллея — feminine

Because длинная аллея is part of the subject of the sentence, so it is in the nominative case.

The whole subject is:

• этот сквер и длинная аллея

Since аллея is feminine singular nominative, the adjective must match:

• длинная аллея

You would get длинную аллею only if it were a feminine singular accusative direct object, for example:

• Я вижу длинную аллею = I see a long alley

Because Если Вы любите тихие места is a subordinate clause, introduced by если (if), and Russian normally separates it from the main clause with a comma:

• Если Вы любите тихие места, Вам понравятся этот сквер и длинная аллея.

This is standard Russian punctuation.

Yes. Russian word order is more flexible than English word order.

This version is natural:

• Если Вы любите тихие места, Вам понравятся этот сквер и длинная аллея.

But you could also say:

• Если Вы любите тихие места, этот сквер и длинная аллея Вам понравятся.

The basic meaning stays the same, but the emphasis shifts slightly. Putting Вам earlier can highlight to you a bit more, while putting the subject earlier can highlight the places themselves.