You can send pieces of a garment even though they are not sewn together. These can even be made of kilayim as long as they are hard and can be sat upon on Yom Tov. However, shoes with spikes or pieces of shoes are prohibited. R’ Yehuda says you cannot send white shoes as nobody would wear them without having them dyed.

Beitzah 2:1

You cannot cook from Yom Tov, which came out on an erev Shabbos, for Shabbos. However, you can cook for Yom Tov and whatever is left can be used for Shabbos.

You can make a special cooked dish before Yom Tov and depend on it to cook for Shabbos [eiruv tavshilin]. Bais Shammai says two cooked dishes are required, Bais Hillel says one cooked dish. They all agree a fish and egg on top of it are considered two cooked dishes.

If these cooked dishes were lost or eaten before Shabbos, then you are prohibited to cook on Yom Tov for Shabbos. If there is a portion the size of an olive left, the eiruv is still good.