Is the word olhando the same in Brazilian and European Portuguese?

No

While the word "olhando" carries the same fundamental meaning (the gerund of the verb olhar, meaning "looking" or "watching") in both dialects, there is a significant difference in typical usage regarding grammar.

In Brazil, the gerund (gerúndio) is the standard way to express an ongoing action (e.g., "estou olhando"). In Portugal, the standard construction for continuous actions is the preposition a + the infinitive (e.g., "estou a olhar"). While a Portuguese person would understand "olhando," it sounds distinctly Brazilian and is much less common in daily European Portuguese speech.

Brazilian Portuguese Usage (Gerund)

1. Eu estou olhando as fotos no meu celular. (I am looking at the photos on my cell phone.)
2. O que você está olhando com tanta atenção? (What are you looking at with so much attention?)
3. Ela passou a tarde olhando a chuva pela janela. (She spent the afternoon watching the rain through the window.)
4. Eles estão olhando o cardápio para decidir o que pedir. (They are looking at the menu to decide what to order.)
5. Pare de ficar olhando para mim desse jeito! (Stop looking at me like that!)

Continental Portuguese Usage (Preposition + Infinitive)

1. Eu estou a olhar para as fotografias no meu telemóvel. (I am looking at the photos on my mobile phone.)
2. O que é que estás a olhar com tanta atenção? (What are you looking at with so much attention?)
3. Ela passou a tarde a olhar para a chuva pela janela. (She spent the afternoon watching the rain through the window.)
4. Eles estão a ver o menu para decidir o que pedir. (They are looking at the menu to decide what to order.)
5. Deixa de estar a olhar para mim desta maneira! (Stop looking at me this way!)