Accent marks can be used to avoid ambiguity in those cases when words are spelled the same but pronounced differently and have different meanings. Eg. доро́га (road) v. дорога́ (short female adjective); бо́льшая v. больша́я and so on. That's recommended (especially in books and media), but not grammatically required.

Except for disambiguation (explained earlier, though it is usually easy to distinguish the cases for native speaker and thus accents are usually not put) accent marks are often used in books for children and for language learners to make it easier to read, because there is no general rule in russian (like in spanish) which sylable to stress - you just have to learn the words. And yes, letters й ё щ are just different letters, we can't call them letters with accents etc. They should be distinguished from и е ш. But sometimes in books or periodic ё is written like е and it is not considered a mistake.

The letters ё, щ and й look like other Russian letters with accent marks, but they are not. They are different letters of their alphabet. The closest thing they have to accent marks are two letters in their alphabet, ь (мягкий знак, soft sign) and ъ (твёрдый знак, hard sign). They are not pronounced, but they tell you to pronounce the previous letter "soft" or "hard." It's kind of hard to describe in text what that means so I suggest typing words with and without ь and ъ in Google Translate (e.g. семь/съесть, мощность/штат) and listening to the very slight difference. I shamelessly admit, that is how I learned to pronounce these letters.