The things you describe sound suspiscious, but it is also true that some people suffer some loss of the abilities due to old age. This is the insidious nature of dementia - it's very hard to tell when you reach that point where the alarm bells should start ringing. Certainly we dismissed my father's forgetfulness as being nothing.
Does your Nan display anything else? These might be: replacing words with "fillers" during conversations (for example, repetetive use of something like"wass-name" in place of real words); losing the sense of time (confusing morning with evening, not knowing what day it is, and so on); loss of short-term memory (eg forgetting having just had breakfast, or repeatedly asking the same question). More worrying symptoms might be strange beliefs/behaviors - such as people being in her house, saying "someone" is "stealing" things or "moving" them, putting things away in odd places (clothes in the fridge say) ,speaking as though someone long deceased is still alive, etc.
It might be that Nan is simply losing some of her abilities through sheer old age - and maybe not. One thing - if she is struggling with conversations, is her hearing OK?
As has been said, all you can do is note down everything that is worrying you, and present these to her doctor. Most doctors won't discuss a patient with anyone else, but I don;t think there's any reason why a relative/friend should not raise health concerns.
If the symptoms are sufficient, the GP might be willing to "invite" your Nan for a "regular checkup" on some pretense or other. At that point the GP could ask some questions (such as - what day is it, who is the Prime Minister, what did you have for breakfast) and based on those decide whether further investigation is needed. There are conditions which give the same symptoms as dementia and they have to be eliminated.
But you can't force Nan to see her GP. Sadly the idea that "there's nothing wrong with me" is very common; it is due to lack of insight (Nan really believes there is nothing wrong, and that she is perfectly normal) and denial. The idea of losing one's faculties is very frightening.
it occurs to me that the annual flu jabs are due soon. This would be an ideal opportunity to get Nan to the GP's surgery, at which point the GP could "ask to see her". Most people regard the GP as an authority figure and are reluctant to say "no" to them!
As to diet - well, it's not good, but if Nan is not actually starving then there is not much point in pressing her about it. With someone of that age the usual advice is, I believe, to worry about getting enough calories in rather than a balanced diet.
Our CPN has said that lots of her patients have very poor diets. My dad at the moment is refusing to eat anything except jam sandwiches (no crusts), biscuits and sweets! He constantly worries about eating anything "in case I get a blockage" and keeps saying "I don't go to the toilet, I must be constipated" and demands laxatives!
We know that he isn't open to reason, is unlikely to actually starve - so we decided not to worry about it! It is a battle that cannot be won, so there is no poit in starting it.
