Snälla: Snella or snaella?
The Swedish course's voice says snaella (with the a a bit exaggerated, but I looked the word up on forvo.com and the pronounciation was snella without the exaggerated a. Which is correct?
In this case, yes. In some cases like "här" and "där" , it's pronounced like the "a" in "bat".
I believe "e" and "ä" are both pronounced like "e" in "bet", except before "r" when they are both pronouned like "a" in "bat".
The distinction between short "ä" and short "e" is rather moot in many dialects, including the Stockholm one. In particular, you will find that many speakers pronounce "hätta" and "hetta" almost, if not completely identically. I think the "e" sound in "bet" is an appropriate English equivalent.
However, the long versions of "ä" and "e" are two quite different sounds. Long "ä" is similar to "a" sound in "bat", while long "e" is... well, imagine a stereotypical Scottish way of saying "play". That long vowel sound (not the diphthong you would say in standard English) is what long "e" should be like.
And just for completeness sake, a vowel is long if it is in a stressed syllable and followed by no more than one consonant, otherwise it is short.
There is a short version and a long version of each Swedish vowel.
In "snälla", the "ä" is short. And the short "ä" is pronounced like the short "e", for example like "e" in well or bell.
Note though that the long "ä" differs from the long "e":
for example hel (= whole) and häl (= heel) don't have the same pronounciation