Večer
I've learned Slovene in elementary school so I don't have quite the academic knowledge of it. More of a sense for it. Therefore I cannot tell you whether there are regularities in pronunciation of Slovene, but I'd say there aren't many. At least as far the vowels are concerned. Anyway, regarding schwa in večer, there isn't any. It's a regular e as you assumed. Can you share a link to an electronic version of SSKJ if you have one?
It's at http://bos.zrc-sazu.si/sskj.html . I think I have found out a way to judge whether there is a schwa but that will only work if there is a Slavic etymology. It seems that schwa only appears when there was a yer vowel (ь or ъ) there before, or as an epenthetic vowel to break up a group of consonants after a word-final yer was lost (like in dober). I also think that SSKJ assumes all unstressed e's are real e's, and notes explicitly when they are not.
Thank you for the link. I don't think you are right about SSKJ explicitly noting schwas. For example exactly the entry for dober [1] doesn't contain a schwa.
No but it is implied because the e drops in the inflected forms. It is targeted towards Slovenes who presumably are aware that only schwa drops in this manner, but true e will stay.
Although I don't know if schwa e always drops in inflected form, it sounds reasonable that it does. Do you know by chance what the second form (the inflected) stands for? For example for dober it reads: "dóber dôbra -o". Is it dual nominative? It remains as the only possible alternative when excluding all the invalid ones.