期限 and 期間: deadlines and periods
Distinguish a time limit from the span between a beginning and an end.
Setting the limit
期限 is read きげん and refers to a time limit for something required or permitted. 「提出期限は金曜日です」 says that the submission deadline is Friday.
「期限を過ぎました」 says that the deadline has passed. It does not establish whether an extension or late submission is allowed.
Describing the span
期間 is read きかん and refers to a span of time between a beginning and an end. 「研修期間は二週間です」 says that the training period is two weeks.
「期間中は何度でも利用できます」 says that the service may be used any number of times within the period. Check the rest of the notice for its start and end.
Reading application notices
「受付期間は一日から十日までで、申込期限は十日の午後五時です」 gives both the application period and the final cutoff time. Distinguish the last date of the period from its specific cutoff time.
期限 can appear with a duration, as in 「期限を一週間延ばす」, extending a deadline by one week. A duration does not automatically require 期間; consider whether the limit is being moved or the entire span described.
Can you determine the exact end date from 「利用期間は一か月です」 alone?
Show the answer and why
No. It only gives a one-month duration. You must also check the start date and how the end is determined to know the exact date.