Is expiation for an oath (kaffarat yameen) required in the following two cases: first, for breaking an oath to continue memorizing with a friend after reaching a certain page, and second, for breaking an oath to start work at a specific minute by starting several minutes earlier?

If you swore to memorize from a specific page and you did not do so, then you have broken your oath and must offer expiation for it. As for the second question, an oath is judged by the intention behind it. As long as your intention was to urge haste and start work early, then you do not break your oath by starting before the time you swore upon.