1) Both me and my wife are currently on H1B working for different companies. Is it possible for my wife to open a consultancy firm (company Y) in partnership with a friend who is a PR, assuming that my wife does not actually work for Company Y?
Sure.
2) Is it possible for my wife to reap financial benefits in form of dividends/income from that company provided she is only an investor and in no way responsible for managing the day to day activities of the company. Her friend who is a PR will be responsible for making all those decisions.
Yes.
3) I work as a consultant for X company, can I have another H1 to work part-time for my wife's company say for working 20 hours a week for the same kind of job profile that I am currently in?
Yes. The H1 would have specify concurrent work (otherwise, CIS may consider it a transfer.)
Do you see any reason that the INS would refuse a H1 petition for that?As long as the job is a specialty occupation that requires a college degree, and you have at least that college degree, no.
Be aware, though, that you can't get a GC through a company you or a relative own more than 5% in.
4) Would a partnership firm be the best way to get into this business?
Well, that really depends. There are lots of considerations that have to go into selecting a company structure. Each has pros and cons, and it is up to the investors to weigh these. An outside person can not say what the best way is.
The IRS gives some starting points for selecting the company structure:
http://www.irs.gov/businesses/small/article/0,,id=99336,00.html