>> Unfortunately we cannot change our accommodation, it's not refundable :(. So, we decided to do as follows: 2 days walking around Zurich ... **Note that on the 3rd day (last day) our flight home is at 8pm.
Even if your accommodation is in Zürich, a half day, or a day at the most, is plenty of time to see the old town and maybe do a short cruise on the lake. I would save it until your final day.
I would still recommend you spend most of your time in the countryside. The rural villages with their traditional buildings and the alpine scenery are what makes Switzerland so special, not so much its cities.
>> and one full day to go to Titlis Mountain.and Engelberg (early in the morning). On the way back we also pretend to stop in Luzern for a quick overview if we have enough time.
That will be a wonderful day. Going early is a good idea, but check the weather and visibility first, in case it is completely foggy on top and there are no views:
It's good to have a backup plan in case the weather is unsuitable, so you don't waste time wondering what to do next.
I wouldn't spend too much time in Engelberg itself after your Titlis visit, but rather head back to Luzern and spend more time there. Engelberg is in a valley, so you have some mountain views - pleasant but not spectacular. In my opinion, Engelberg lacks the charm of more traditional alpine villages such as Wengen, Grindelwald and Mürren in the Jungfrau Region, where traditional wooden chalets are the predominant building style, rather than the modern low-rise apartment blocks that are quite a feature of Engelberg.
The main sights in Luzern are close to the railway station. The "City Guide" PDF on the page below has a map with a self-guided walking tour marked. It's across two pages, so viewing the PDF in "Two Page View" makes it easier to see.
Frommers also has directions for a walking tour:
www.frommers.com/desti nations/lucerne/walkin g-tours
A nice way of going back to Zürich is to go via Arth-Goldau. The train travels high along a hillside on the eastern side of the Zugersee, and you have scenic views down to to the lake, lakeside villages, and the mountains (including the Rigi) on the other side of the lake. Sit on the left, and then later on the right as you travel along the Zürichsee (Lake Zürich). Sunset will be between about 17:30 and 18:10, depending on when in February you will be there, so if you decide to go back that way, you would want to do it before dark.
>> Do you think we should consider buying the Tell Pass and make the most of it, using the 2 days even though we would have to spend extra 65CHF? - Or do you think we should take no Tell Pass and try to discover Zurich more peacefully and not rushing and spend one day only in the Alps?
Most people choose the cheapest option for their plans as a whole, but there is also a lot to be said for paying a bit more for convenience. That's a personal choice. Don't forget about the free travel for 15-year-olds (under certain conditions) that I mentioned in my previous post.
As I said above, you will be missing a lot if you spend so much time in Zürich.
>> Is there any other option in this itinerary you would suggest?
To reiterate, I would spend only your last day in Zürich, and do day trips on the other days. But in the end, it's your holiday, so spend your time where you think you will get the most enjoyable experience :-)