1) Someone told me that we cannot read the Quran while wearing slippers or shoes. is that true? the person said that it is disrespectful therefore we should not read while wearing footwear.

2) My skin is very oily. Is it necessary for me to remove the oil before I do my wuzu? If I do wuzu on an oily face, is my wuzu invalid (as the oil may act as a barrier between water and skin)?

1-No it’s not true you can recite Quran.
2- It will not considered barrier and your Wudhu is valid.