Learn Spanish (Latin America): Estamos aprendiendo una técnica muy interesante. - We are learning a very interesting technique.

You can only use llevamos if you also include an amount of time. For example, Llevamos dos semanas aprendiendo una técnica muy interesante (We have been learning a very interesting technique for two weeks). Because this sentence doesn't mention how long the learning has been happening, you must use estar + gerund (estamos aprendiendo) to simply say what you are doing right now.

Why doesn't the adjective interesante change to interesanta to match the feminine noun una técnica?

Adjectives that end in -e in Spanish are gender-neutral. They stay exactly the same whether they describe a masculine or feminine noun. You would only change it by adding an -s if the noun were plural, like in unas técnicas interesantes.

Is técnica related to the English word 'technique' or 'technical'?

It translates to both depending on how it is used! As a noun (like in this sentence), la técnica means 'the technique.' But it can also be an adjective meaning 'technical.' When used as an adjective, it does change to match gender and number, like in un problema técnico (a technical problem).

What is the infinitive form of aprendiendo, and how is this gerund formed?