No. There are always taxis outside the hotel. A taxi one way should be no more than 15 euros
Sorry, I don't know but the airport in Lisbon is not far from downtown and taxis are not expensive...
Yes, please contact reception. But do not expect a deal price.
I don't know. You should contact the hotel. In general I am sure they can organize it.
Don't think so. Beware that taxi might not accept creditcard.
I think they have but it is much more expensive. Taxis are readily available and they are quite safe. I only paid 12 Euro from airport to hotel.
Get an answer from InterContinental Lisbon staff and past guests.