Yes I believe so.

I had a good deal of luggage and I didn't find it a difficult walk. The incline is extremely minor (especially for Seoul),your parents should have no problem if they are comfortable with walking on a daily. I stayed 10 days. I had an above average room on a higher floor. The King size bed does take up most of the sleeping area compared to American hotels, but not to the point where it was a problem moving around the space or managing luggage. The breakfast is nice, coffee is always in the lobby, and the staff is most helpful with almost any request I had.

I felt that it was very easy to walk to major shopping spots -- the subways are connected underground and the walkways are lined with shopping stalls! I think it took us about 10-15 minutes to walk to Myeongdong which is a major shopping area that was open late and also had food options open late. I'm not sure about halal food options specifically, but there is a lot of variety -- definitely easy to eat vegetarian and vegan. I didn't find it particularly clear from the outside of food places what options they had for particular diets (but I also don't read korean hangul)! TripAdvisor reviews for particular restaurants may be helpful!

You can take a airport bus #6001 or #6015, get off at Numdaemun Market. then around 10 min walk. Search Youtube "6015 LIMOUSINE BUS STATION(NAMDAEMUN MARKET) to HOTEL SHINSHIN " It show how to walk to the hotel. Have a nice trip