Yedid Nefesh is the traditional shalosh seudos melody as sung by R' Sucher Shelley z"l. Transcribed and sung here by Dov Dukhovny. Click here for sheet music and a short explanation from Dov.
Baruch Hashem Yom Yom is a traditional shabbos table song sung by R' Motty Weinstock. See the complete ArtScroll Siddur, page 494.