Attack timer stops after killing enemy (when attack script loose target)

Hey guys! I have a problem, I have attack script with cooldown and stuff in it, I've created basic combat system, everything works until I kill enemy, it destroys it as intended but then my attack timer stops counting until I select another enemy. Also I keep getting an error until I select first enemy because target field in attack script is empty at start.

Scripts:

Attack Script:

 using UnityEngine;
 using System.Collections;
 using UnityEngine.UI;
 
 public class BasicAttack : MonoBehaviour {
 
     public GameObject target; //target to attack
 
     public int damage;
 
     public float range = 4;
     public float attackTimer;
     public float cooldown = 2.0f;
 
     public GameObject damageNumber;
     public GameObject cooldownImage;
     public Text cooldownText;
 
     Targeting t;
     UserInterface UI;
 
     void Start () {
 
         cooldownImage.SetActive(false);
 
         attackTimer = 0;
 
         t = FindObjectOfType<Targeting>();
         UI = FindObjectOfType<UserInterface>();
     }
 
     void Update () {
         
         float distance = Vector3.Distance(target.transform.position, transform.position); //calculating distance
 
         cooldownText.text = attackTimer.ToString("F0");
     
         if (attackTimer > 0) {
             attackTimer -= Time.deltaTime;
         }
         if (attackTimer <= 0) {
             attackTimer = 0;
         }
         if (Input.GetKeyUp("1")) { //attack key
             if (attackTimer == 0 && distance < range) {
                 Attack();
                 attackTimer = cooldown;
                 //damage numbers
                 var clone = (GameObject)Instantiate(damageNumber, t.selectedTarget.GetComponent<EnemyAI>().hitPoint.position, t.myTransform.rotation);
                 clone.GetComponent<DamageNumbers>().damageNumber = damage;
             }
             else {
                 Debug.Log("Target is out of range!");
             }
         }
         else {
             cooldownImage.SetActive(true);
         }
 
         if (attackTimer == 0) {
             cooldownImage.SetActive(false);
         }
     }
 
     public void Attack() {
 
             float distance = Vector3.Distance(target.transform.position, transform.position); //calculating distance
 
             Vector3 dir = (target.transform.position - transform.position).normalized; //calculating direction
             float direction = Vector3.Dot(dir, transform.forward); //calculating direction
 
             if (distance < range) { //making player not be able to attack if too far
 
                 if (direction > 0) { //making player not be able to attack if target not in front of him
                     EnemyHealth eh = (EnemyHealth)target.GetComponent("EnemyHealth"); //getting enemy health
                     t.selectedTarget.GetComponent<EnemyHealth>().TakeDamage(-damage); //adjusting enemy health
 
                     UI.infoText.text = "";
                 }
                 else {
                     Debug.Log("Target needs to be in front of you!");
                 }
                 UI.infoText.text = "";
             }
             else {
                 Debug.Log("Target is out of range!");
             }
     } //attack
 }

EnemyHealth Script:

 using UnityEngine;
 using System.Collections;
 
 public class EnemyHealth : MonoBehaviour {
     
     public float maxHealth = 100;
     public float curHealth = 100;
 
     CombatTargetUI ct;
 
     void Start () {
         ct = FindObjectOfType<CombatTargetUI>();
     }
 
     void Update () {
         TakeDamage(0);
     }
 
     public void TakeDamage (int ad) {
         curHealth += ad;
 
         if (curHealth <= 0) {
             curHealth = 0;
             /*ct.HideUI();*/
             Die();
         }
         if (curHealth >= maxHealth) {
             curHealth = maxHealth;
         }
         if (maxHealth <= 1) {
             maxHealth = 1;
         }
     }
 
     void Die () {
         
         StartCoroutine(TimeToDestroy());
     }
 
     IEnumerator TimeToDestroy () {
         yield return new WaitForSeconds(0.5f);
         ct.HideUI();
         Destroy(gameObject);
     }
 }

Targeting Script:

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 public class Targeting : MonoBehaviour {
 
     public List<Transform> targets;
     public Transform selectedTarget;
 
     public Transform myTransform;
 
     CombatTargetUI ct;
 
     void Start () {
         targets = new List<Transform>();
         selectedTarget = null;
         myTransform = transform;
 
         ct = FindObjectOfType<CombatTargetUI>();
 
         AddAllEnemies();
     }
 
     public void AddAllEnemies () {
 
         GameObject[] go = GameObject.FindGameObjectsWithTag("Enemy");
 
         foreach (GameObject enemy in go) {
             AddTarget(enemy.transform);
         }
     }
 
     public void AddTarget (Transform enemy) {
         targets.Add(enemy);
     }
 
     void SortTargetsByDistance () {
         
         targets.RemoveAll(target => target == null);
         targets.Sort(delegate(Transform t1, Transform t2) {
             return Vector3.Distance(t1.position, myTransform.position).CompareTo(Vector3.Distance(t2.position, myTransform.position));
                 });
     }
 
     void TargetEnemy () {
 
         if (selectedTarget == null) {
             SortTargetsByDistance();
             selectedTarget = targets[0];
         }
         else {
             int index = targets.IndexOf(selectedTarget);
 
             if (index < targets.Count - 1) {
                 index++;
             }
             else {
                 index = 0;
             }
             DeselectTarget();
             selectedTarget = targets[index];
         }
         SelectTarget();
     }
 
     void SelectTarget () {
 
         ct.ShowUI();
 
         selectedTarget.GetComponent<Renderer>().material.color = Color.red;
 
         BasicAttack ba = (BasicAttack)GetComponent("BasicAttack");
         ba.target = selectedTarget.gameObject;
     }
 
     public void DeselectTarget () {
         if (selectedTarget != null) {
             selectedTarget.GetComponent<Renderer>().material.color = Color.white;
         }
 
         selectedTarget = null;
     }
 
     void Update () {
 
         if (Input.GetKeyDown(KeyCode.Tab)) {
             TargetEnemy();
         }
     }
 }

I think that those are all scripts that might cause problem, can anyone help me? I'm desperate. :(