Is Fatimah's saying, may Allah be pleased with her, "And my father resembles the Prophet, not Ali" considered an oath by her father, and is it permissible to swear by other than Allah?

This statement is not an oath, for an oath is made with the bare waw (و) devoid of the alif (ا), and the object of the oath comes directly after the waw, such as "wal-lahi" (والله - by God). As for the waw here, it is for exclamatory wonder, as mentioned by Ibn Hisham in "Mughni al-Labib" and al-Zabidi in "Taj al-Arous". They cited the poet's verse: "Wa bi-abi anta wa fukal-ashnab Ka'annama dhurra 'alayhil-zurnub" (O, by my father, you and your moist mouth As if saffron was sprinkled upon it). This verse has been attributed to Abu Bakr, may Allah be pleased with him, in some sources.