Mi hermano anda tocando el cable de la lámpara y me pone nervioso.

Both are possible, but they do not sound exactly the same.

• está tocando = a neutral progressive: he is touching / messing with it right now
• anda tocando = often suggests someone is going around doing something, often repeatedly, casually, or in a way the speaker finds annoying

So Mi hermano anda tocando el cable... can sound a bit like:

• My brother keeps messing with the lamp cable
• My brother is there fiddling with the lamp cable

In Spain, andar + gerund is very common for this kind of nuance.

Andar + gerundio is a verbal structure that often expresses an action that is:

• ongoing
• repeated
• somewhat casual, aimless, or irritating
• sometimes spread over a period of time rather than just one exact moment

Examples:

• Anda diciendo tonterías. = He goes around saying stupid things.
• Ando buscando mis llaves. = I’m looking for my keys / I’ve been looking for my keys.

In your sentence, it makes the brother sound like he is fiddling around with the cable, not just touching it once.

Here it means touching, handling, or messing with.

The verb tocar can mean different things depending on context:

• tocar la guitarra = to play the guitar
• tocar algo = to touch something
• no tocar = don’t touch

Because the object is el cable de la lámpara, the meaning is clearly touching / fiddling with the cable, not playing in the musical sense.

This is the normal Spanish way to express possession between objects.

• el cable de la lámpara = the lamp’s cable / the cable of the lamp

Spanish often prefers de where English might use a possessive or a noun-noun combination.

More examples:

• la puerta de la casa = the door of the house / the house door
• el motor del coche = the car’s engine

So de la lámpara simply identifies which cable we mean.

Because mi hermano already has a possessive adjective (mi), and Spanish normally does not combine that with a definite article in this kind of sentence.

So you say:

• mi hermano
• mi madre
• mi coche

not normally:

• el mi hermano ✘

This works the same way as in English: my brother, not the my brother.

Because poner + adjective is a very common Spanish pattern meaning to make someone become a certain way/state.

• me pone nervioso = it makes me nervous
• me pone triste = it makes me sad
• me pone contento = it makes me happy

Using hacer here is generally not the natural choice. Spanish usually says:

• Eso me pone nervioso. rather than
• Eso me hace nervioso. ✘

So poner is the idiomatic verb for causing an emotional state in this context.

Because me shows who is affected.

• me = me
• te = you
• le = him/her
• nos = us

So:

• me pone nervioso = it makes me nervous
• te pone nervioso = it makes you nervous

Without me, the sentence would be incomplete because we would not know who is being made nervous.

It agrees with the person who is feeling nervous, not with hermano and not with lámpara.

So if the speaker is male, you say:

• me pone nervioso

If the speaker is female, you say:

• me pone nerviosa

That is because the adjective describes me, the speaker.

Not always. Nervioso often means:

• anxious
• uneasy
• tense
• on edge

In this sentence, it means something like:

• it makes me nervous
• it makes me anxious
• it gets on my nerves a bit

Because someone is touching a lamp cable, the feeling could be worry, tension, or irritation.

Yes, depending on context.

Literally, it means it makes me nervous, but in everyday use it can suggest:

• anxiety
• discomfort
• irritation
• being on edge

In this sentence, if the speaker is worried something bad might happen, it is close to it makes me nervous. If the focus is annoyance, it may overlap with it gets on my nerves, though that exact English idea is more directly expressed with phrases like:

• me saca de quicio
• me pone de los nervios

Because it links two actions/events:

1. Mi hermano anda tocando el cable de la lámpara
2. me pone nervioso

So the structure is:

• My brother is messing with the lamp cable, and it makes me nervous

The subject of the second part is understood from the first situation. Spanish often leaves that kind of subject implicit when it is obvious from context.

Yes, in a broad sense the whole situation caused by the brother makes the speaker nervous. But grammatically, the second clause most naturally refers to the action/situation:

• my brother messing with the lamp cable makes me nervous

Spanish often allows this kind of implicit subject. It does not have to repeat a pronoun like eso.

You could make it more explicit by saying:

• Mi hermano anda tocando el cable de la lámpara y eso me pone nervioso.

Yes, it sounds natural, especially in spoken Spanish from Spain.

In particular:

• andar + gerundio is very common in Spain
• me pone nervioso is completely natural
• tocar el cable clearly means touching / fiddling with the cable

A very neutral alternative would be:

• Mi hermano está tocando el cable de la lámpara y me pone nervioso.

But the original sentence has a more vivid, colloquial feel.

Yes. Depending on the tone, Spanish offers stronger or more specific verbs:

• Mi hermano está manoseando el cable de la lámpara...
  = My brother is handling/fingering the lamp cable...
• Mi hermano está trasteando con el cable de la lámpara...
  = My brother is fiddling with the lamp cable...
• Mi hermano no para de tocar el cable de la lámpara...
  = My brother won’t stop touching the lamp cable...

The original anda tocando already suggests mild annoyance, but these alternatives can make that even clearer.