R’ Tarfon only allows olive oil since other oils are not drawn as well to the wick and involve a concern of shema yateh (Tosfos). R’ Yochanan Ben Nuri challenged this by pointing to the people of Bavel who don’t have access to olive oil; but how does this inaccessibility mitigate the fact that it is assur on account of shema yateh?
The Gemara advises one to instruct his household gently ‘so that they accept from him’. The Rosh cites the Gemara (Gittin 6b) that a person should never instill excessive fear in his home. This reason would indeed seem a sufficient basis for our Gemara as well; why does the Gemara provide the reason of ‘acceptance’ instead?
The Gemara located a Tanna who holds ’Ein Bereira’ by a Derabanan – from the Braisa of Techumin. Tosfos explains that we could not prove this from the Braisa of Maaser, since although Maaser of vegetables is Derabanan, nevertheless the concept of Maaser is rooted in Torah, and is therefore (perhaps ) more stringent. But isn’t Techumin also rooted in Torah, according to the opinions who hold that the Twelve Mil limit is min hatorah?