Unwanted surface on top

Question

I am new to blender and I am following a tutorial for making a coffee cup. On a particular part of the cup, there are no mesh connections and hence the surface is emphasized as another colour.. and on rendering that part is seen as a hole.

I've tried to merge vertices but a lone vertex appears on the middle of the surface and is not helping. Also the coffee cup handle is a mess(I used the spin tool). Can I fix it through sculpting(I tried but not helping)?

I've attached all necessary pictures below:

Answer 1

The following is "fixing" only, as there are few bad things in your model.

For the handle, you have inner faces, that should be deleted (only did 2 in the gif below):

Also have inverted faces. You can see that activating face orientation, then use ShiftN to solve it (except for the last issue, see below):

The handle also has inner part that should not exist: remove them.

Last step, the face that is bad. It is a ngon. Probably you did after removing some parts.

So delete the bad parts and use existing one to replace it.

Can do it by selecting a good slide, duplicate and rotate it ShiftDR and adjust as closely as possible to the bad part.

To do it, make sure the 3D cursor is placed at the center and it is the origin point for the rotation, also, use snap with increments (see what is surrounded by green below):

Once all slices are recreated, select all A and merge duplicates M then "by distance" (tune the distance in the operator panel to be sure to remove the wanted doubles).

Again, this is fixing only, and you'd better redo it all as exercise.

All these done, you should have a cup with no more cracks: