From my hotel to the castle of Prague

Can you walk? it is about 1 1/2 miles, and a nice walk. Moreover, taking a transit route will require walking at least 1/3 that amount. You can see how much walking is involved you put these locations into Google Maps and click on transit options.

it is a fairly steep uphill walk.
walk to Starometska and then take the 2 or 18 tram over the river to Malostranska ,just one stop then take the 22 or 23 tram up the hill.You can get off at Prasky Hrad stop where the majority of tourists get off ,but this is also where the tour buses let folk off and the security lines can be quite long. alternatively take the tram 2 more stops to Pohorelec and then it is an easy stroll down hill to the castle,the lines at the security to the left of the main gates here are in my experience seldom busy.

Thank you so much both of you for your answers.To be honest, my friend cannot walk really well because he has got spasticity in one leg.I mean, he can walk but not as well as the rest of us.So I believe the best option is to take the tram number 2 and stop at Proholec.Can we buy tickets on the train?

you can't buy on the tram and must have a ticket to ride, your hotel will probably be able to sell you some or any Relay shop or tabak shop. Might be worth considering a 24 hr ticket as you can the validate it once and jusmp on an off trams at your leisure.
https://livingprague.com/prague-transport/prague-public-transport/
this link explains getting around.

There are at least two types of single tickets. The ticket good for 30 minutes (including transfers) costs 24 korunas. The 90-minute ticket cosrs 32 korunas. You can go pretty far in 30 minutes. The 90-minute ticket is of course necesary for getting to and from the airport.

Thank you once again both of you for the tickets information.The link was really useful.Just two last questions please and then I will leave you alone, ha ha.
1) The tram which stops at Prohorelec is number 2 or 22? Just to be sure.
2) How do I get by public transport to Petrin, which is a hill, I think.
Thank you once again for everything.

The tram number is 22 and it is not proholec or proholerec but Pohorelec and "r" has that little v above and that changes pronunciation to something like Pohorzelec. To Petrin if you want to avoid steep incline go by the funicular which goes from the tram stop Ujezd. Tram (or metro) ticket is valid there.

sorry about my spelling.
The funicular up the hill is easy enough to use but if heading to Petrin tower bear in mind this is a building site at the moment, the tower is open but there is a huge amount of work going on in the area completely re-landscaping the area, new paths and new buildings going up. the lovely new toilets have opened up there but it is going to be quite a while till things are completed. there is a café inside the tower and a small beer/food stand just outside but not a great deal of room outwith the building areas.

Thank you very much llJa and Unclegus for your answers and time.I really appreciate it.I hope I wll not bother you again :)

happy to help.

Me too. Unclegus, you spelled it correctly. vannosgeorge, we are here to be "bothered".

I am really happy then you got "bothered" :)