> Tattoos
The teaching in Leviticus 19.28 doesn't apply to the way tattoos are used today. What was going on in Lev. 19 was tattooing the body as part of a religious ritual. Such markings may have been designed to protect a person from the spirits of the dead or to demonstrate membership in a cultic group. There is nothing morally wrong with tattooing. These practices were part of heathen rituals, and that's what the problem was. The marks were usually in honor of some idol, and they were forbidden because they were signs of pagan worship. Even the context (the first part of the verse) shows us that cultic practices are what was in mind. Nowadays tattoos are a body-decorating fad and have nothing to do with the heathen rituals/pagan worship that the Bible forbids.
> shaving your beard
In Walton, Matthews, & Chavalas's
The IVP Bible Background Commentary p. 134:
"For men hair has symbolic value as a sign of manhood or virility (see 2 Sam. 10:4). Women decorate their hair and groom it carefully as a sign of beauty. The prohibition against trimming the “sides of your head” or the “edges of your beard” uses the same terminology as in Lev 19:9-10, which deals with the harvesting of fields. In both cases an offering is involved—one to the poor and the other to God. The law’s placement here immediately after the prohibition against divination suggests that the restriction on cutting the hair is based on the Canaanite practice of making an offering of hair to propitiate the spirits of the dead (see Dt. 14:1). Hammurabi’s code #127 penalizes false witnesses by having half the person's hair cut off. The Middle Assyrian Code #44 allows a debt slave's master to pull out his/her hair as punishment (see Neh. 13:25). Both laws suggest that shame is attached to the loss of hair. There is a Phoenician inscription from the 9th century reporting the dedication of shaven hair by an individual in fulfillment of a vow made to the goddess Astarte. Hair (along with blood) was one of the main representatives in ancient thinking of a person’s life essence. As such it was often an ingredient in sympathetic magic. This is evident, for instance, in the practice of sending along a lock of the presumed prophet’s hair when the prophecies were sent to the king of Mari. The hair would be used in divination to determine whether the prophet’s message would be accepted as valid."
This has nothing in common with 1 Corinthians 11.