Ja tack would work if the question is "would you like some more?" Ja, snälla would not work there as snälla only is used in a pleading was. If I'm freezing and someone asks if they may close the window the correct answer would be "Ja, snälla!" A thank you would work but not be as strong.
I'm a little cofused here. I think I remember from my Swedish course (though that was years ago, so it could be wrong), that "snälla" refers to the person you ask and means literally something like "dear". For example a child asking their nanny: "Snälla Anne, få jag...?" - "Dear Anne, may I...?", or me asking my boyfriend "Kan du öppnar fönstret, snälla?" - "Can you open the window, love?" So it sounds totally awkward to me putting "snälla" at the end of sentences in not-so-intimate communication frames. But maybe I remember it wrong?
Snäll means kind, so you're appealing to the other person's kindness. The constructions we use in Swedish don't always translate well directly to English, so translating it as please often fits better. One example where a direct translation works is "Vill du vara snäll och..."
For example: "Vill du vara snäll och ge mig en kaka?" translates to "Would you be kind and give me a bisquit?"
Not to be confused with "vänligen", which means "kindly" and is much more formal and not often used in speech.
Example: "Vänligen gå ej på gräset" - "Kindly don't step on the grass".
Vänligen is more formal, and snälla is usually used more in a pleading sense. They also usually have different constructions.
Snälla mamma, kan jag få en glass? - Please mom, may I have an icecream?
Vänligen ta ner fötterna från bordet. - Kindly take your feet off the table.
Coincidence! I was talking about "Snälla" with my Swedish-born husband just this morning (same day as ChristyBon2's post!!). He said he remembers it as "Snälla du". When I said I learned just "Snälla" here, he thought maybe the phrase had changed in the decades since he was in Sweden. Google Translate also suggests with "Snälla du" for "please". Good thing we found out that just "Snälla" isn't ideal.
while studying the Pimsleur language cd the instructor says "snalla" is the polite way to ask for something, example: "I want something to eat" is not "jag vill har nagot atar" but the polite way to ask is "jag vill snalla har nagot atar." (Please excuse my typos, still learning.)
That is not right! 'I want something to eat' would be Jag vill ha något att äta, and if you have to put snälla into that sentence, please don't put it in the middle like that, it sounds totally wrong. The polite way could be to say Jag skulle vilja ha något att äta 'I would like to have something to eat', or Skulle jag kunna få någonting att äta? 'Could I have something to eat?' You can put snälla before the last one and it sounds OK: Snälla, skulle jag kunna få något att äta? 'Please, could I have something to eat?'
Okay, this blows my mind, as I learn languages by thinking in those languages, so the literal translation for "Jag skulle vilja ha något att äta" would be "I should want to have something to eat" or for "Skulle jag kunna få någonting att äta?" would be "Should I be allowed to have something to eat?"
Mind blowing, but that's my method :))
I think I disagree with you about what would be literal translations for some words: what first comes to mind for skulle is would, whereas for should my first Swedish translation is borde. And the first literal translation for få is definitely get: the meaning receive is much more central than the meaning be allowed to. Possibly this also points to pitfalls in the method itself, but it is an interesting method from some points of view and to an extent I think it always goes on in our minds (while most people would argue that the ideal is to get away from it as soon as possible).
Edit: I realized I misunderstood your rewrite of the sentence, but kunna isn't well translated as be allowed to either, if you want a literal translation for it, that should be be able to.