What is wrong with my orbit sim equations? How can I fix them?

Question

Edit: Partial question: The object now moves in an ellipse like it's supposed to, but it orbits around a different point than I intend. How can I make it orbit around a particular object at a point?

New Code:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class Orrery2 : MonoBehaviour
{
    public Transform Center;
    public Transform Other;
    float x;
    float y;
    float z;
    float Begining = 1;
    float Elapsed;
    float dE = 0;

// Update is called once per frame
void FixedUpdate()
{
    Elapsed = Begining++;
    PositionFromDate(100f, 0.8f, 1f, 2f, 2f, 2f);
    Debug.Log(Elapsed);
    Debug.Log("x:" + x + ", " + "y:" + y + ", " + "z:" + z);
    Other.transform.position = new Vector3(x, y, z);
}
void PositionFromDate(float a, float e, float i, float W, float w, float M)
{
    M = M * Elapsed;

    //Newton's Method
    float E = M;
    while (Mathf.Abs(dE) < 1e-3)
    {
        dE = (E - e * Mathf.Sin(E) - M) / (1 - e * Mathf.Cos(E));
        E -= dE;
        Debug.Log("E:" + E + ", " + "e:" + e + ", " + "M:" + M + ", " + "dE:" + dE);
    }

    //Determine P and Q, 2d coordinate system in plane of orbit
    float P = a * (Mathf.Cos(E) - e);
    float Q = a * Mathf.Sin(E) * Mathf.Sqrt(Mathf.Abs(1 - Mathf.Pow(e, 2)));

    Debug.Log("Line 46 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);

    // rotate by argument of periapsis
    x = Mathf.Cos(w) * P - Mathf.Sin(w) * Q;
    y = Mathf.Sin(w) * P + Mathf.Cos(w) * Q;

    Debug.Log("Line 52 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);

    // rotate by inclination
    z = Mathf.Sin(i) * x;
    x = Mathf.Cos(i) * x;

    Debug.Log("Line 58 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);

    // rotate by longitude of ascending node
    float xTemp = x;
    x = Mathf.Cos(W) * xTemp - Mathf.Sin(W) * y;
    y = Mathf.Sin(W) * xTemp + Mathf.Cos(W) * y;

    Debug.Log("Line 65 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);
    }
}

The question below was answered

This is in c# in Unity. The intent of the script is to move a sprite around a 2-body orbit. Instead it pops around erratically and rapidly speeds off into the distance. I based most of this off of this other question, but I removed a lot of the conversions from the jpl database in the beginning of the script because I intend to use generated numbers on a larger scale. I don't know much about these maths, so I can't tell what is wrong.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class Orrery2 : MonoBehaviour
{
    public Transform Center;
    public Transform Other;
    float x;
    float y;
    float z;
    float Begining = 1;
    float Elapsed;
    float dE = 0;
    //a: Semi-Major Axis
    //e: Eccentricity
    //i: Inclination
    //W: Longitude of the Ascending Node
    //w: Argument of Periapsis
    //M: Mean Anomaly
    //E: Eccentric Anomaly



    void FixedUpdate()
    {
        Elapsed = Begining++;
        PositionFromDate(1f, 0.8f, 10f, 2f, 2f, 2f);
        Debug.Log(Elapsed);
        Debug.Log("x:" + x + ", " + "y:" + y + ", " + "z:" + z);
        Other.transform.position = new Vector3(x, y, z);
    }
    void PositionFromDate(float a, float e, float i, float W, float w, float M)
    {
        a = a * Elapsed; //Semi-Major Axis
        e = e * Elapsed; //Eccentricity
        i = i * Elapsed; //Inclination
        W = W * Elapsed; //Longitude of the Ascending Node

        //Newton's Method
      float E = M;
        while (Mathf.Abs(dE) < 1e-3)
        {
            dE = (E - e * Mathf.Sin(E) - M) / (1 - e * Mathf.Cos(E));
            E -= dE;
            Debug.Log("E:" + E + ", " + "e:" + e + ", " + "M:" + M + ", " + "dE:" + dE);
        }

        //Determine P and Q, 2d coordinate system in plane of orbit
        float P = a * (Mathf.Cos(E) - e);
        float Q = a * Mathf.Sin(E) * Mathf.Sqrt(Mathf.Abs(1 - Mathf.Pow(e, 2)));

        Debug.Log("Line 46 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);

        // rotate by argument of periapsis
        x = Mathf.Cos(w) * P - Mathf.Sin(w) * Q;
        y = Mathf.Sin(w) * P + Mathf.Cos(w) * Q;

        Debug.Log("Line 52 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);

        // rotate by inclination
        z = Mathf.Sin(i) * x;
        x = Mathf.Cos(i) * x;

        Debug.Log("Line 58 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);


        // rotate by longitude of ascending node
        float xTemp = x;
        x = Mathf.Cos(W) * xTemp - Mathf.Sin(W) * y;
        y = Mathf.Sin(W) * xTemp + Mathf.Cos(W) * y;

        Debug.Log("Line 65 " + "a:" + a + ", " + "e:" + e + ", " + "i:" + i + "W:" + w + ", " + "w:" + w + ", " + "M:" + M + ", " + "E:" + E + ", " + "P:" + P + ", " + "Q:" + Q);
    }
}