Your first question is just semantics. How do you define a new species? Textbook definition would be when it can no longer breed with the original species. I don't think this will quite apply to the future of human evolution. I don't think you will able to define the point at which a physical subgroup is formed until well after it has already happened. For now, transhuman is just a statement of philosophical identity.
Your second question is something I think about nearly every day.
Initially, the techniques necessary to extend life may be limited to the
very wealthy, but market forces being what they are, I think prices would
rapidly fall once established. Biological techniques are notoriously easy
to copy once the correct protocols are identified. People will demand to
have the product, even if they have to put themselves in debt for eternity
(literally) to get it. Accumulating wealth is probably a good idea is any
case though. I'm not particularly materialistic, but wealth is one of the most valuable tools for survival - it allows you breathing room in times of crisis.
The government is probably the least likely source to ever fund these techniques. On the contrary, if we are to achieve the goal of reversing aging, one of the biggest roadblocks will be the regulatory agencies of big government. Government vested interests are in maintaining order. These techniques, once perfected, will cause one of the most radical shifts in culture humanity has ever seen - not something any government will look forward to with glee.
Your earlier question is something I struggle with constantly as well. I feel we are within 10-15 years of a first stage breakthrough in halting aging. I have grandparents in their 70's who I am very close to. They are very progressive for people of their generation, so I have been trying to gently suggest cryonics. I don't think it is the best option, but for now, it is the only one. Vitrification techniques announced this year are tremendously better than anything that has been used so far - the neural tissue preservation was nearly perfect in rabbits. I'm am very optimistic about the likelihood of reconstruction if you have good structural preservation.
"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." R.A. Heinlein