I wouldn't say "normal." It's made clear that Miss Marple has taken in dozens of young women who are orphans or from poor families, and trained them to be first-rate maids. Many employers barely treated their maids as human, but others treated certain servants as members of the family. I think that Miss Marple does see some of her maids as the daughters she never had... or perhaps it would be more accurate to describe them as honorary nieces.
I think it is "normal" because she wouldn't want to seem too unapproachable to her employees in order to get the best out of them and it worked because she kept in touch with some after they left her.
I can't say if it's normal or not. But Miss Marple is an eldery lady, no kids. She lives in a small village, so it's usual to have more tenderness or a close relation to the others, including the maids than in a big city. Besides, some of the maids play an important role in some stories, so I think this makes their relation more close and caring.
I think there was at play the sense of noblesse oblige which would have governed relationships between the gentry and their staff, tenants, or members of the 'lower' social orders who lived in the village. The way in which that ancient relationship of dependence survived into the 20th century is alluded to in Agatha Christie's Mrs McGinty's Dead. The postmistress urges the young woman who has evidence to go to Mr Summerhayes to receive a sympathetic and knowledgeable hearing. Agatha Christie tells us that he belonged to the old order, his ancestors had lived at the big house for generations, and she was looking up to him for guidance. The old order which survived for longer in the country was more supportive than the employer/ employee relationships of the industrial revolution towns, where the sense of moral duty to, yes, lord it over, but, yes, also to protect was a serious concern for an honourable person. There is definitely something kinder about Miss Marple's guiding interference than could be expected from other well-born characters. When you read Jerry's references to the servants as he narrates The Moving Finger, you see that he scarcely notices them, is bored with being appealed to by his housekeeper for advice on the poison pen letters. He also says things such as he has seen a woman in a mop cap shuffling backwards when he comes upstairs and has assumed that she is the new maid. He speaks of 'something' in a cap and apron answering the door, and he seems, at the end of the novel, scathing about the value of the SPOILER ALERT Symington's maid and her life, saying that she wasn't that happy, so, too bad she is dead kind of thing, but it isn't the end of the world. This is not to say that he didn't value life, but he does not enter as empathetically into the concerns of those who look up to him as Miss Marple would, and lacks her humanity - and Poirot's humanity. I think the contrast here underlines the skill of Agatha Christie's characterisation, and the way that her writing will inhabit a character and portray their responses with consistency, not going all out to make them perfect, even when they are narrating.
I should have expressed more clearly that the countryside retained the old social divisions and the squire of a rural village had a duty to protect his tenants and guide them. The squire was usually a magistrate, like Colonel Protheroe in Murder At The Vicarage, and that sense of having a duty to guide the lower orders was very strong. You were to have power, but you must not misappropriate it for your own self-advancement: it was yours to use for the greater good of the community, Miss Marple is kind to her maids, but not slow to correct them. You can see from the comments of the vicar in Murder at the Vicarage about his maid that many maids were getting out of that job scene, where you lived in the house, often, and were told when you could come and go. They were seeking better paid shop work, but there would not have been the same level of personal care and solicitude in the new job: your boss wouldn't have so readily have given you compassionate leave if you had a problem, or have given you some good condition clothes to supplement your own wardrobe. Maids would be fed by the employer, so would have been a part of the household, so a well-regulated intimacy would be bound to develop. Other posters mention Enid Blyton. If you read her children's story about the poison pen letters, you see that Fatty and his friends are sympathetic to one maid who had received one, and want to help her and understand her: their sense of superiority is tempered by genuine kindness and a wish to understand, and this era would be Christie era, the 40s and early 50s. Blyton was susceptible to critical censure of her treatment of working class characters, and, by the mid 50s, was changing her stories to have some less well-educated sleuths, and a lot more egality weaving through the plots. You see with Miss Marple that she changes her attitudes as society changes.
At that time, In large houses maids were trained by the housekeeper and cook. They progressed from tweenies (in between maids) to housemaids to personal maids. A woman of restricted means like Miss Marple had only one servant, and she had to train her herself, because a trained maid demanded higher wages (and prefered to live in a city or town). What is special is the kind and thoughtful way she treats her maids - not only training them, (with a lot of encouragement), but also advising them and their friends, coming to their aid, and knitting garments for their babies when they marry and have children. No wonder her old servants love her and want to take care of her (like the one she stays with in 4.50 from Paddington). Miss Marple isn't the only old lady to have good relations with her servants - in The Moving Finger, while it is true that Jerry treats the servants as something useful, half invisible and certainly not interesting or worthy of respect or compassion, (though he is just as callous about Mrs. Symington's death as he is about Beatrice's death) Miss Emily goes to live with a former servant who is very protective of her and cossets her - so she must have had a very good relationship with her.
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