You need an HDRI texture for the proper reflections you are looking for. Go into the shading tab and switch from object shading to world shading (highlighted below). Add an environment texture, and assign an HDRI texture
(If you need HDRI images, one place that has a good selection of free ones is here - https://hdrihaven.com/hdris/).
Alternatively, if you want the same ones that come with blender (used in lookdev), they are in the folder
../2.82/datafiles/studiolights/world. I think the one you used in the preview is
Connect it up as shown below and enjoy.
For the other problem you are having, your (base) material node setup should look like this. Either add the nodes if they're not there, or if you want to just start again, hit the minus button next to the material, and add a new one.
EDIT: A SAMPLE PROJECT FOR YOU
Ok, I made a .blend project that SHOULD be pretty much the same as what you're working with. It works fine for me. Download it, and have a look, and see if it
a) it works for you, and
b) has any differences between it's settings and yours.
File is here -