the tilt of the axis makes it winter most often
Because the orbit of the moon is tilted at an angle of 5 degrees to the ecliptic.
The relative position in the sky (relative to the Sun) is completely related to the phase. For example, at full moon the Moon will be opposite the Sun (an angle of almost 180 degrees), at new moon it will be near the Sun (an angle near zero degrees), and at half-moon it will be at a 90 degrees angle.
The angle between the orbit planes of the Earth and the Moon is known as the inclination. It is approximately 5.1 degrees.
The angle of a crescent moon is determined by the relative positions of the Sun, Earth, and Moon in space. It is a result of the sunlight reflecting off the Moon, with the angle changing as the Moon orbits the Earth and moves in relation to the Sun.
That happens at half-moon, when the Moon is at the right-angle of a right-angled triangle. The acute angle of the triangle is at the Sun and it is only 0.147 degrees on average. At half-moon you can look at the Moon, and the Sun is approximately 90 degrees to the right or the left, depending on whether the Moon is waxing or waning.
5.14 degrees.
That happens at half-moon, when the Moon is at the right-angle of a right-angled triangle. The acute angle of the triangle is at the Sun and it is only 0.147 degrees on average. At half-moon you can look at the Moon, and the Sun is approximately 90 degrees to the right or the left, depending on whether the Moon is waxing or waning.
The moon is in its first quarter phase. It's moved about a quarter of the way around its orbit since the new moon. The sun, moon, and Earth form a right angle (90 degrees) during this phase, causing half of the moon facing Earth to be lit up and the other half to be dark.
Nothing happens
Imagine an angle, with the Earth at the vertex and the sun and moon on the two rays. -- New Moon . . . the angle is zero. -- Crescent phases . . . the angle is acute. -- First Quarter and Third Quarter . . . the angle is 90°. -- Gibbous phases . . . the angle is obtuse. -- Full Moon . . . the angle is 180°.
15 degrees
20 degrees.