Q1. What is your prima facie opinion - whether STP or SHF
A: I have an annual half fare card but that's because I often visit Switzerland more than once a year and generally travel on the main line rail, bus and boat routes and don't visit too many of the 'tourist trap' destinations. I would recommend the STP for your type of holiday.
Q2. But what happens when you reach city train station and going to your hotel by local public transport like bus or tram,
A: concur with ildiko. You won't get the 'free card' until you book into your accommodation.
WARNING: you must study carefully and/or be prepared for disappointment: a few city travel cards issued by hotels in main cities give useful free travel, but many 'guest cards' issued are of little value, for example offering a free coffee but only if you have purchased a very expensive meal.
EXAMPLE: In February 2020 we were issued with a lovely glossy guest card at a hotel near Klosters, part of the 'Davos-Klosters' area. It looked great until in the small print we saw that free local train travel was only available if the guest card is issued by a hotel in Davos! It turned out that we could hardly use any of the so called 'special offers/reductions'
Q3. If you are visiting any city and not staying in that city, whether day pass for public transport is available
A: most large towns and cities across the whole of Europe (and beyond) with comprehensive public transport networks offer some sort of 1 day or 24 hour pass (or reduced cost multi journey card). It doesn't matter one bit where you arrive from
Q4. When you are buying train ticket on SBB website, it shows half fare (assuming you are having SHF) and many fares for different timed train. But when you are buying ticket, it does not show any specific time and shows date. Does it mean you can take any train on that date
SHF gives you the flexibility to purchase a half fare ordinary point to point ticket at any time, right up to 30 seconds before a train leaves (I've done that a few times...) I normally use platform ticket machines.
Q6. Do you mean half fare card means half fare on all train tickets, lake cruise, attractions, local public transport etc. Are there any exceptions
No attractions included, SHF is essentially a transport discount card (see also my comment above)
Q7. Instead of Bernina Express, If I take normal train and complete the journey, is it doable. How I can travel from Tirano to Lugano in this case
The Tirano - Lugano bus is the only way. It is a fairly recent invention to cater for the increasing number of tour groups from outside Europe, in the past all tourists tended to go to Tirano and back both ways on the Bernina railway. Both ways on the train can be nicer than having to use a bus.
Q8 Any easy hiking trail open in May
Loads. I have visited Switzerland almost every year at the Easter holiday time and have done many long hikes even up to higher altitudes - if you mainly stay in valleys. A good way to hike in Switzerland is to take a train to a station, get off and walk back, or walk on to the next station. This can be done all over Switzerland