Если оса летает рядом, лучше не махать руками.

This is a very common motion-verb question.

• летать = to fly around, fly repeatedly, buzz about, move in different directions
• лететь = to be flying in one direction, to be in flight toward somewhere

In this sentence, the wasp is not imagined as flying from point A to point B. It is buzzing around nearby, so летает is the natural choice.

So:

• оса летает рядом = a wasp is flying/buzzing around nearby
• оса летит would sound more like the wasp is flying in a specific direction

Here рядом means nearby / close by.

In this sentence, it works as an adverb:

• Если оса летает рядом = If a wasp is flying nearby

You may also see рядом с + instrumental, meaning next to something:

• рядом с домом = next to the house

But in your sentence, there is no noun after it, so it simply means nearby.

Because this is an impersonal advice construction.

• лучше не махать руками literally means it is better not to wave your hands
• It sounds like general advice or a warning

This is softer and more general than a direct command.

Compare:

• Лучше не махать руками. = It’s better not to wave your hands.
• Не маши руками. = Don’t wave your hands.
  This is a direct command to one person.

Russian often uses лучше + infinitive to give advice in a natural way.

Because махать usually takes the instrumental case for the thing being waved.

So:

• руки = nominative/accusative plural
• руками = instrumental plural

In Russian, the idea is closer to to wave with the hands.

Other examples:

• махать рукой = to wave one’s hand
• махать руками = to wave one’s hands / flail one’s arms

So руками is required by the verb here.

Because the sentence means waving your hands/arms in general, usually both of them.

Russian often uses the plural here when talking about this kind of physical motion:

• махать руками = wave your hands / flail your arms

If you said махать рукой, that would usually mean wave one hand.

Here лучше is not an adjective like лучший (best). It is the comparative form used as a predicate, meaning:

• better
• it is better to...

So:

• лучше не махать руками = it’s better not to wave your hands

This use of лучше is very common in advice:

• Лучше подождать. = It’s better to wait.
• Лучше не спешить. = It’s better not to hurry.

Because Russian often leaves it unstated when the meaning is general or obvious from context.

• лучше не махать руками naturally means it’s better not to wave your hands
• The sentence is giving general advice to whoever is in that situation

If you want, you could make the person explicit:

• Если оса летает рядом, тебе лучше не махать руками. = If a wasp is flying nearby, you’d better not wave your hands.
• ...вам лучше... = ...you’d better... (formal/plural)

But leaving it out sounds very natural.

Not necessarily. The singular is often used in Russian for a general situation.

So Если оса летает рядом... means something like:

• If a wasp is flying nearby
• If there’s a wasp buzzing around near you

It describes a typical situation, not necessarily exactly one specific wasp in a strict numerical sense.

Russian often uses singular nouns this way in advice and general statements.

Yes.

Если introduces a subordinate clause:

• Если оса летает рядом = if a wasp is flying nearby

Then the main clause follows:

• лучше не махать руками = it’s better not to wave your hands

Russian normally separates these with a comma:

• Если оса летает рядом, лучше не махать руками.

Yes. Russian word order is flexible, though the original version is very natural.

Original:

• Если оса летает рядом, лучше не махать руками.

Possible variation:

• Лучше не махать руками, если оса летает рядом.

Both are grammatical. The difference is mainly about emphasis and flow:

• starting with Если... sets up the situation first
• starting with Лучше... gives the advice first

The original sounds especially natural for a warning or instruction.

Yes, but the nuance changes a little.

• махать руками = wave your hands, move your hands around
• размахивать руками = wave your arms around, flail them, swing them broadly

So размахивать is often more vivid or stronger. In this sentence:

• лучше не махать руками sounds natural and neutral
• лучше не размахивать руками sounds like don’t wave your arms around wildly

Both are possible, but махать руками is simpler and more general.