Did Jesus have nails through His feet?

No, not His feet.

Only once it is said that nails were driven through His hands (John 20:25), never that they were driven through His feet.

The feet of Jesus are mentioned as He appears to the eleven, who were just listening to the report of the two men who met Him the day before on the road to Emmaus (Luke 24). Because they think He might be a ghost, he points out that ghost would not have hands and feet sticking out of his tunic. He does not expose His hands and feet to show the wounds.

Psalm 22 makes mention of pierced feet (v 16), and although this Psalm predicts much of the crucifixion, some elements remain unapplied (like the bulls of verse 12, the dogs of verse 16 and the out-of-joint bones of verse 14). We do not know if the pierced feet of Psalm 22 can be applied to Jesus.

We also don't know whether His arms were horizontal or vertical on the cross. The Bible seems to find these issues not very important.