If you are applying for a design patent:
The lid and cup are protected as a whole.
No need
There is no patent infringement. If its other shapes are similar to yours and just add a handle, the cups and cup lids it produces will infringe.
It depends on whether the replacement part is similar or identical to the one you applied for patent.
If you are applying for an invention (or utility model patent)
First, it depends on the point of your invention, and secondly, it depends on how to write your claims.
There is no need to apply separately, you can write it in the claims (even if you meet the patentability of both, you can apply for both in one patent)
Same as above, apply A patent is not an infringement, it is only an infringement if the product meets the characteristics of your claim;
If you have sole rights to write the cup body and lid, then no matter how you change them, as long as you apply for a patent The features in are all considered infringement.
However, a utility model is a new technical solution proposed to protect the shape and structure of a product or its combination that is suitable for practical use. I'm wondering if the lid or body of your cup is satisfactory.