cancellation within 14 days.

They will always try it, but to be true they dont have the right since the law os clear when it says that the during the 14 days you can cancel the service without costs.

They are saying there is a new law 15-2016 which states they can charge installation costs 350.00 euro which must be paid before cancellation, also I haven't signed any contact with them.

They have right to that costs during the fidelization period only after the free resolution period. Any contract made from distance as 14 days of free resolution, where free means really free.
https://www.anacom-consumidor.pt/-/direito-de-livre-resolucao

The regulator clearly states that is has no penalization, @Fórum can you explain why are NOS trying to charge a consumer in the free resolution period?

By the way, you should consider to write in the https://www.livroreclamacoes.pt/Pedido/Reclamacao so you get a proof of the request, they are possibly only slowing you down to deny your right. Very common for NOS in my experience.

Hello @Karen P,

Thank you or reaching out to us. We’ll assist on solving this matter.

Please send us a private message to the @Fórum profile with your NOS Costumer Number or taxpayer number.

Thank you