1. “И” or “ѝ”
ѝ (with an accent) is a pronoun – дадох ѝ книгата (I gave her the book). и without an accent is a conjunction – ти и аз (you and I). If you cannot find the accent on your keyboard, that is no reason to write “й”. That is a different letter.
2. The full article
See the separate page. In short: градът е хубав, но отивам в града (the town is nice, but I'm going to the town).
3. “Не” with verbs
With verbs, always separate: не искам, не зная, не мога (I don't want, I don't know, I can't). The exceptions are verbs that do not exist without “не”: ненавиждам (I hate), негодувам (I am indignant).
4. Joined, hyphenated, separate
- всъщност, наистина, изобщо (actually, really, at all) – written as one word
- вагон-ресторант, северозапад (dining car, northwest) – check the dictionary, not your intuition
- по-хубав, най-голям (nicer, biggest) – “по” and “най” always take a hyphen
5. Double “н”
Странни, истинни, единни (strange, true, united, plural) – when the root ends in “н” and a suffix with “н” is added. But истински (genuine) has one “н”, because there is no second suffix there. The language does not promise to be logical.
6. “-ия” and “-ие”
Кашкавал от Германия (kashkaval cheese from Germany), but желанието ми е (my wish is). Remember: -ия for feminine, -ие for neuter.
7. Capital letters
Months and days are written with a small letter: понеделник, януари (Monday, January). So are nationalities: българин, германец (a Bulgarian, a German). English habits don't help here.
8. Numbers
Двама мъже, две жени, два стола (two men, two women, two chairs). For male persons there are special counting forms: двама, трима, четирима (two, three, four). „Два мъже“ is not a crime, but it sounds as if you had counted them in a warehouse.
9. Agreement
Ние бяхме доволни (we were satisfied), but Вие бяхте доволен? (were you satisfied?) – if you are politely addressing one man. Yes, this is an official rule, and yes, it is a little confusing.
10. “Във” and “със”
във and със are written before words that begin with “в”/“ф” or “с”/“з” respectively: във Варна, със сестра си (in Varna, with my sister). In all other cases: в София, с брат си (in Sofia, with my brother).
The official source is the Official Orthographic Dictionary of the Bulgarian Language from the Institute for Bulgarian Language at the Bulgarian Academy of Sciences (БАН). If someone corrects you with “that's just how it's said”, ask them for the number of the rule. The conversation usually ends there.