My solution for the first and last child challenge

const Btn_toggleList = document.querySelector('.Btn_toggleList');
const listDiv = document.querySelector('.listDiv');
const input_Description = document.querySelector('input.description');
const p_Description = document.querySelector('p.description');
const Btn_Description = document.querySelector('button.description');
const listUl = document.querySelector('ul');
const input_addItem = document.querySelector('input.addItem');
const Btn_addItem = document.querySelector('button.addItem');
const lis = listUl.children; 

// function: add 3 btns for list items
function attachListItemButtons (li) {
  let up = document.createElement('button');
  up.className = 'up';
  up.textContent = 'Up';
  li.appendChild(up);

  let down = document.createElement('button');
  down.className = 'down';
  down.textContent = 'Down';
  li.appendChild(down);

  let remove = document.createElement('button');
  remove.className = 'remove';
  remove.textContent = 'Remove';
  li.appendChild(remove);
}

//function: remove the first btn (up btn)
function rmvUpBtn (li) {
      let upBtn = li.children[0];
      li.removeChild(upBtn);
      console.log('removeup');
};

//function: remove the second btn (down btn)
function rmvDownBtn (li) {
      let downBtn = li.children[1];
      li.removeChild(downBtn);
      console.log('removedown');
};

//function: add up btn back
function addUpBtnBack (li) {
      let upBtn = document.createElement('button');
      upBtn.className = 'up';
      upBtn.textContent = 'Up';
      let downBtn = li.firstElementChild;
      li.appendChild(upBtn);
      li.insertBefore(upBtn,downBtn);
      console.log('addUpBtnBack');
};

//function: add down btn back
function addDownBtnBack (li) {
      let downBtn = document.createElement('button');
      downBtn.className = 'down';
      downBtn.textContent = 'Down';
      let removeBtn = li.lastElementChild;
      li.appendChild(downBtn);
      li.insertBefore(downBtn,removeBtn);
      console.log('addDownBtnBack');
};

// function: update list
function updateList () {
  if ( lis.length > 1 ) { //ckeck: if the number of list items more than 1
    const lastLi = listUl.lastElementChild;
    const firstLi = listUl.firstElementChild;

    for (let i = 0 ; i < lis.length ; i ++ ) {
      if (lis[i] !== firstLi && lis[i] !== lastLi ) { //check: if this item is not the first NOR the last item
        if ( lis[i].children[0].className === 'down' ) { //check: if the first element of the li is 'down', add 'up' btn back
          addUpBtnBack(lis[i]);
        } else if ( lis[i].children[1].className === 'remove' ) { //check: if the second element of the li is 'remove', add down btn back
          addDownBtnBack(lis[i]);
        }
      } else if (lis[i] === firstLi) { //check: if this is the first item, remove up btn
        if (lis[i].children[0].className  === 'up') {
          rmvUpBtn(lis[i]);
        }
      } else if (lis[i] === lastLi) { //check: if this is the last item, remove down btn
        if (lis[i].children[1].className === 'down') {
          rmvDownBtn(lis[i]);
        }
      }
    }

  } else if (lis.length === 1 ) {
    let li = lis[0];
    rmvUpBtn(li);
  }
  console.log('updateList');
};

// function: initialize list(attach btns and update list)
function initialize () {
  for (let i = 0 ; i < lis.length ; i ++ ) {
    attachListItemButtons(lis[i]);
  };
  updateList();
};

initialize();

// event listener： up, down, remove btn
listUl.addEventListener('click', (event) => {
  if (event.target.tagName === 'BUTTON') {
      if (event.target.className === 'remove') {
        let li = event.target.parentNode;
        let ul = li.parentNode;
        ul.removeChild(li);
      }
      if (event.target.className === 'up') {
        let li = event.target.parentNode;
        let prevLi = li.previousElementSibling;
        let ul = li.parentNode;
        if (prevLi) {
          ul.insertBefore(li, prevLi);
        }
      }
      if (event.target.className === 'down') {
        let li = event.target.parentNode;
        let nextLi = li.nextElementSibling;
        let ul = li.parentNode;
        if (nextLi) {
          ul.insertBefore(nextLi, li); //(li, nextLi.nextSibling) will do
        }
      }
      //update list after pressed any btns in the list
      updateList();
  }
});

// event listener： change description btn
Btn_Description.addEventListener('click', () => {
 p_Description.textContent = input_Description.value + ':'; // either use 'innerHTML' or 'textContent'
 input_Description.value = '';
});

// event listener： hide and show btn
Btn_toggleList.addEventListener('click', () => {
  if ( listDiv.style.display === 'block' ) {
    listDiv.style.display = 'none';
    Btn_toggleList.textContent = 'Show List';
  } else {
    listDiv.style.display = 'block';
    Btn_toggleList.textContent = 'Hide List';
  }
});

// event listener： add item btn
Btn_addItem.addEventListener('click', () => {
  let ul = document.getElementsByTagName('ul')[0];
  let li = document.createElement('li');
  li.textContent = input_addItem.value;
  ul.appendChild(li);
  attachListItemButtons(li);
  input_addItem.value = '';
  updateList();
});

addItemButton.addEventListener('click', () => {
  let ul = document.getElementsByTagName('ul')[0];
  let li = document.createElement('li');
  li.textContent = addItemInput.value;
  attachListItemButtons(li);
  ul.appendChild(li);
  addItemInput.value = '';
  hideButtons(lis);
});