For organization and specification, it can be really useful to know exactly when battles took place to be able to understand and examine the political, military, economic, social, etc. aspects that led up to, were changed or influenced by, etc. to the dates or events that took place or followed.

For sake of mind, however, knowing just the year can be more applicable when giving an overview of the scope of the war, especially when examining the complex and vast history of the War.

Not a strange question at all. Important yes to have an understanding of the dates, not to the point where it is providing you stress.

So on the "it is important" front, as has been mentioned, it is helpful to know "this happened before this event" as provides context and understanding of why people took decisions, outcomes, what led to events and how decisions/events influenced what came after. So dates matter but I would suggest not worrying too much about it that it causes you stress.

One of the books you may have on the subject could have a time-line of major events somewhere near the start, feel free to copy that down or bookmark it as something you can quickly and easily consult for major events/dates. If you need a date not on there for a moment, check sources or a quick search online will usually serve your purpose.

Learning does require repetition but that should come naturally enough anyway in your studies. Any time you read a book or other source, or look something up, dates will likely get mentioned. Each time it does, that date being repeated further sinks into your head until it becomes imprinted. That study will hopefully provide the repetition for dates.

If you really want to have a set of dates memorized quickly, a timeline borrowed from a book would hopefully be more manageable and provide a structure of dates. But I wouldn't put too much emphasis on it at this point, perhaps better to keep studying and learning and let it build from the studies.