Whether you can or can't in reality is moot, unfortunately. The literature search in biomedical fields should indeed be theoretically reproducible. I don't know about other fields, but it would seem odd to me if a search was not reproducible, that would lead to a very arbitrary literature selection.

As for the experiments, yes, in experimental fields. But in all (most?) fields, including non-experimental, the whole process should be well documented so it could be reproduced end-to-end if possible. If it's not reproducible there should be good, well explained reasons why not.

Note that reproduciblity does not necessarily mean the exact same answer will definitely emerge, just that the methods can be followed closely.

Yes, you must be able to reproduce the results. If reproduction is not possible, the work lacks scientific validity.