Yes!
It is possible and usually expected for a single gene/gene product to
be associated with more than one GO term. The fact that you may have
found that there are two or more different GO terms associated with a
single gene/gene product in your results should not be a cause for
concern.
The Gene Ontology allows users to describe a gene/gene product in
detail, considering three main aspects: its molecular function, the
biological process in which it participates, and its cellular
location.
For example, the homeobox D9a gene product from zebrafish has numerous
GO terms associated with it. Each term describes details about this
gene’s molecular function, localization in the cell, or its
involvement in certain biological processes. One GO term explains that
this gene product carries out the molecular function of selectively
interacting with DNA (DNA binding), while a different GO term explains
that this gene product is found in the nucleus of the cell.
Trying to write one single term that describes in detail everything
about a gene/gene product in a single statement would require the
existence of as many terms as genes there are - for all species - in
the planet. This would be very unpractical and not easily scalable.
Instead, the use of ontologies help us organize information in a way
that allows researchers to use the same term to describe a
characteristic that is shared by more than one gene product (e.g. all
the genes involved in the process ‘translation’), and more than one
term to describe all the characteristics of each gene product, as in
the example above. This is a reason why you would see more than one GO
term associated to a single gene/gene product.
To answer your specific questions, a single gene product can definitely have multiple annotations in the same aspect (Function, Process, or Component). The same goes for the individual aspect: a single gene product's annotations can map back up to several different terms in the same aspect. A rather ubiquitous protein might have annotations to GO:0005737 cytoplasm AND GO:0005634 nucleus; a subunit of a complex might have an annotation to a child term of 'protein-containing complex' and an annotation to GO:0005634 nucleus, especially if it is not obvious from the complex where the protein might be functioning. A good way to mentally justify this is to remember many proteins have multiple functions and may do any of those functions in various areas of the cell- performing rather unrelated functions is called 'moonlighting'.
a gene for sure is implied in biological processes, cellular components and molecular functions, and yes, it could be more than one.