Judy - I understand entirely what you mean, being similarly an elderly adult. I have heard good things about the following hotel complex which you can book online through poe helping to support them at the same time. Click on the following link for more details: http://www.picturesofengland.com/England/Greater_London/Radisson_Edwardian_Heathrow
As for the 'per adult, per stay' question. Suppose there are two of you and your hotel costs £100 per night, per adult and you stay 1 night. That means the cost will be £200 in total for your 1 night 'stay'. It doesn't mean that you pay the same total if you stay longer. Another example would be if two of you stayed 3 nights at £100 per adult, the total for your 3 nights 'stay' would be £600
I hope this helps a little. The hotel quoted is not as expensive as that but remember you get your hotel cheaper anyway by booking online through www.picturesofengland/hotels ie the link above, rather than going direct to the hotel. They are special internet only prices through this website.
Need any further help, get back to me. Good luck, safe journey and enjoy your visit!