Since Cancer cells have unlimited growth potential, can they be induced towards totipotency and pluripotency? If so, can cancer cells be used in stem cell culture because of similar properties of unlimited replication? Can they be used in cell lines to culture viruses even?
Cancer cells can be and are used in cell culture. HeLa cells were the first human cell line to be grown in culture and they were derived from a cervical tumor.
That being said, Cancer cell lines would not necessarily be used for stem cell work. They have sustained too many mutations to study the type of questions that stem cells are used to study, though as MattDMo points out, teratomas, tumors that originate from stem cells, can be used in stem cell research as a model for Stem Cells in culture. Also, they could never be used for therapeutic purposes.
As for viruses, HeLa cells were used by Jonas Salk to develop the polio vaccine, so cancer cells are used in viral research.
Edits in italics.
Adding onto AMR's answer, cancer cell lines are used extensively for research. They are typically fast to grow. HeLa Long grow to capacity of a 10cm dish within about 48hours, depending how you split them. Now some lines are different than others and each have their pros/cons but the main thing behind them is they make it possible to view the effects of genes being knocked-down/out in human cells.
As for the use of viruses in cell cultures. They are not only used for viral research but also genomic research.
What is typically done is to introduce a gene into a cell culture line via a retrovirus (called a Retroviral Transfection). It is an extremely effective method of creating a stable cell line with your gene of interest attached to a "fluorescent" gene so you can visualize it in the cell when it gets transcribed. This leads to Immunofluorescence(IF) and many other techniques commonly used today.
You can also introduce a plasmid to cells that contains a shRNA that will "knockdown" the gene you are studying the effects of. This way you can see what happens to cells when this gene is not present (done a lot for study of replication proteins).
The caveat is that sometimes these cell lines can be transient (last only a few passages) or stable. They all also act very differently so typically to "prove your case" that the protein has the function you conclude it to have, you should do experiments with several different cancer cell lines.
Regarding your question about whether cancer cells could be used in studying stem cells:
I have done stem cell work, and we used various teratoma cell lines (which are cancers that resemble germline tissue) in parallel with embryonic stem cells (ES cells) and induced pluripotent stem cells (iPS cells) for various experiments. Of course the choice of experimental system completely depends on what exactly you're studying, but teratomas have proven themselves to be reliable model systems for looking at certain aspects of stem cell structure, function, and differentiation. One of the biggest advantages, at least in the work that I was doing, was that they grew relatively quickly and consistently, while iPS or ES cells can very easily spontaneously differentiate if extreme care is not taken in culturing and passaging them. You don't have to worry about donor-to-donor variation, and they are pretty tolerant to being frozen and thawed.
The work I did was in industry, so unfortunately I can't really get into many details, but I was involved in looking at various transcription factors that are responsible for the maintenance of pluripotency as well as the induction of differentiation, as well as testing various live-cell imaging techniques to track particular differentiation pathways. We made a number of observations using teratomas that directly translated to iPS and ES systems, without all of the overhead that those systems required.