Cookers are a problem: we bought Mother a new cooker with flame safety device, after coming home to kitchen full of gas, but she hasn't been able to learn about holding the knob in. I think I'll try writing a note to stick on the cooker ... but she'd probably decide it was ugly and remove it. She "can't abide" the look of the cooker anyway and doesn't think she's got a grill any more (old one had eye-level grill, illegal to get a new one as it's too near a fixed cupboard under new regs!). Again, solving the safety problem has meant she can't at present cook (but hasn't done much cooking anyway for years, as we're living with her - though she likes to stew rhubarb or apple from the garden, too often forgetting them and burning them). But fortunately she's used a microwave for a long time and is OK with it for heating up meals if we're out for a few hours.
If your Mother can cope with a microwave there are wonderful firms who will deliver once a fortnight straight into freezer - and the meals don't even need to have the plastic pierced, they just go into the microwave. Mother's twin sister, who lived alone, used them and felt she'd done her duty to herself nutritionally (and had a dietetics training so knew what she was about - no dementia there). One with a name conjuring up agriculture in a county west of London was the one she used.
But getting back to question "Can people learn new things": Mother's developed one or two new routines: we got her a commode and she decided to keep it in a spare wardrobe (late father's) and gets it out every night, empties the potty and puts it away every morning, as if she's been doing it for years. When she's in the carehome respite room she can, as far as I know, remember the way back to her room. But she'll look in her diary, see the day centre where she goes 3/week, has been going 3 years, and say "What's xxx? What do I do there? What do I need to take? Do I need to pay?", over and over. Perhaps she can learn by doing, but not learn memories associated with words. I really need to try to help her with the cooker.
It's all so difficult.