Ambiguity in Earth's "Tilt"
The fact that the perihelion is close to the the winter solstice is purely coincidental. The perihelion might occur in any season. It wanders around in a somewhat chaotic fashion because of the gravitational influence of the other planets. At the moment the perihelion moves a day every 58 years.

Let A = Earths axis, and E = the line perpendicular to the orbital plane. The angle between A and E is called the axial tilt. Let S = the line between the centers of the Earth and the Sun. Let P = the plane containing S and E. 

Q1 is (maybe) asking what is the angle between A and P on Jan 2. It will be about 23.4 times sine(2*pi*12/365).  Because there are 12 days from Dec 21 to Jan 2.

Q2. yes.