About 90% of the time it is unnecessary to convert a vector layer to a shape layer. The only reason to do so is to use shape layer animators, animate the actual vector path, or extrude the 3D layer using C4D. For most of the projects, converting AI files to shape layers is a complete waste of time.
If you need to convert Vector layers to shape layers those AI files cannot have any gradient fills or other effects applied. They must be simple filled shapes. Each object you are going to convert to a shape layer should be on a separate layer and the file imported as a composition. If those objects need gradient fills, you'll have to add them after you convert the vector file to a shape layer.
If you absolutely must convert your AI files to vector paths you can either open up all the groups that are created and try and sort things out, or you can return to Illustrator and properly prepare the artwork for the task.
Cropped screenshots and screenshots that you drag and drop to the "Drag and drop here.." field on this forum are useless. Please embed screenshots that show the modified properties of the problem layers using the toolbar or drag them to the form so we can see them. Tell us what your design goal is and we can suggest an efficient workflow.
Let's make it short: You may have watched a ton of tutorials, but it's pretty clear that you never actually have read the online help on which AI features are actually supported for the shape layer conversion. Sorry to be so blunt, but that's all it comes down to. You expect AE to give you the same appearance when in fact stuff like gradients isn't even supported and in order to get best results in AE, files have to be prepared suitably in AI. That and of course @Rick Gerard has a point: People always mistake the conversion as mandatory, when most of the time it isn't even needed and AE can handle native AI artwork just fine. It would really be a good idea if you studied up on the basics first and actualyl read the help instead of relying on videos where a lot of this is skipped over and not explained.