No Excuses

I’m a professional illustrator, I’m from Italy and I work in the UK as a video game artist. I usually just write short stories, nothing too complicated o convoluted. I tend to get bored pretty easily so I’m not exactly the kind of person who can manage to stick to a novel for a decade. (I usually write in Italian so please don’t take my English as an example) So, I recently wrote two short books. The first one is a collection of my grandma’s recipes. I know it’s not something that will change the course of literature, but honestly my initial purpose was purely emotional. I have been told people don’t live forever so I just wanted to gather all her recipes before, well, it was too late, so to speak. Then I realized that maybe a book about the recipes of an elderly Italian woman could have some commercial relevance, at least in Britain. After all the entire kingdom is famous worldwide – as admitted by its own inhabitants - for its not-exactly-top-of-the-range food. Italy on the other hand is famous for the opposite reason so I figured that someone might be interested in it. Anyway, the book is written in a humoristic style, there are a few anecdotes about my grandma’s life and persona (they’re relevant because both vital parts of her cuisine) and as opposed to most cooking books I planned to include a few of my own illustrations rather than the usual photographs of pasta and meatballs.

I'm a children's book editor, so please bear in mind that I'm no expert in food publishing for adults. The things I am thinking now are (and anyone actually in food publishing, feel free to correct me):

• There are a TON of Italian cookbooks available in English already. You have some heavy competition.
• People are more likely to buy a cookbook for its ease, its appetizingness, its novelty, or its personal charm than its type of cuisine.
  
• So that means not only must the recipes be excellent, the stories must be very charming.
  
• And it means the publisher who picks this project up probably will want pretty pictures of the food. But they can handle that photo shoot.

Assuming that the stories are charming enough to make people want to spend some time (and money) on the book, this is an excellent example of a situation in which getting your work edited in advance of submission might be very good for it. Your English is a little bit rocky, and so getting a freelance editor to clean it up for you might help the publisher to whom you send it to see its potential.

The second work is a 500 words picture book. Being an illustrator I couldn’t help picturing the story in my mind in images first, the words came after or at least simultaneously. Let’s say that initially the plot was just an excuse to put together a consistent series of colourful images I would have fun working on, and that at the same time could entertain my toddler girl.
Since I’m not a book illustrator (if we don’t mention the pointless Repair Your Car by Yourself which I illustrated when I was seventeen and for which I wasn’t even credited for) I did some research and I learnt (from you, btw) that editors don’t like authors to submit manuscripts that are already illustrated (or at best they don’t care if they are).
Hence my questions:
Does the same “rule” apply when an author-illustrator submits a manuscripts with his own pictures?

Maybe. Since you are paid for your illustrations, there's a chance that your art is professional enough for you to be considered as an author/illustrator. But the part where you say "Let’s say that initially the plot was just an excuse to put together a consistent series of colourful images" is a big red flag. I've gotten submissions that started as a colorful (but unconnected) series of images, with a text that tried to connect them with something approaching a narrative. Tried and failed. Anytime you're doing something in your bookmaking "as an excuse" for something else in your bookmaking, I strongly suggest you rethink whether there is any excuse for it.

Is it likely (on the unlikely assumption the story is accepted) that the book might get published but illustrated by another artist? To be honest it would be really awkward to be a professional illustrator who gets published for something he did primarily for fun that eventually gets illustrated by someone else.

It's possible, yes. If you couldn't stomach that and are unwilling to consider that option, make that clear in your cover letter.

Does the fact that the story is closely linked to the images decrease the chances of it being published? (assuming the story is good enough but maybe the style is somehow wrong etc.).What I mean is, does the rejection of the illustrations usually imply the rejection of the manuscript in its entirety in this case?

If you say in your cover letter that you'd be willing to consider someone else illustrating your story, then the editor will bear that in mind.

I’m finishing all the illustrations anyway, but do you think in general, when it comes to picture books, an author/illustrator should submit only sketches?

An author/illustrator should submit mostly sketches and a couple pieces of finished art. This is because (a) the art will almost certainly not be accepted just the way you originally envisioned it--that's why publishers expect to see sketches before final art. And (b) we cannot assume what qualities will carry over from an artist's sketches to their final art, and what qualities will only show up in the final art. So you have to send samples.