أرسلَ و بعث generally have the same meaning, you can use both to say "I sent a letter" or "I sent someone to ..."
دراسة is the studying (more general than درس)
درس means ONE lesson, دراسة means the whole studying (session, exams...)
After اندلع we need to use the word fire (حَريق / نار ), but with اشتعل you just need to say the place
نشر (to spread) but here there is someone who did/doing it, unlike انتشر, it means that something is spread but we don't know who is doing it, we talk to rumors for example, desease ...
طَرَقَ = to knock (on the door) / طَلعَ = to come out
إمراة، شابة و فتاة the only difference between them, is the age
فتاة = girl / شابة = young lady / إمراة = a woman / lady
I hope I helped you understanding the difference.