Hello Sam,
Please, see some responses to your questions below:
1) Ipanema/Leblon vs. Copa vs. Botafogo/Catete/Gloria as Investment opportunities. Assume that we have same standards (condition etc.) sizes and plans on offer, but only different locations (disregard beach views etc. anomalies), where do you think that one gets best value per sq meter?
(I hear Botafogo is developing rapidly)
Tough question. You can get more apartment for your dollar in Gloria, but your liquidity is not going to be nearly what it is in Copa or Ipanema. Overall, if you are investing for the sole purpose of making money, you are probably better off looking somewhere else.
2) Can you find a 2-3 bedroom flat in Botafogo in decent condition for R$ 2000 / sq meter?
It is not going to be easy, but it is still possible.
3) How about "lançamentos"? Default risks? Are they overpriced in general?
The risks are there, the construction is generally not as good, and the developer "financing" is definetly factored in into the property price.
4) Construction/renovation/remodeling costs per sq meter in Rio?
Based on my experience, you can spend as little as R$300 per sq. meter on a basic renovation (paint, touch ups...). More serious project, but with no frills (yet would include plumbing and electrical overhaul), would be somewhere in the area of R$750 per sq. meter. Luxury renovation could cost about R$1,000 per sq. meter
5) Do you generally need to apply for rights for remodeling (e.g. changing windows, or building a sauna on the roof top of a cobertura, in my home country this is virtually impossible...) an old apartment? If so, are there any fees/taxes/expenses, or does it take a long time?
It is always easier to ask for forgivness then for permission

Cobertura projects are always messy. Permissions are required from both city authorities and the condo association. Yet, in Brazil nothing is impossible.
6)I am also considering the option of buying something in absolutely crap condition, but with good location and a LOT OF SPACE. (In the end, what does the condition matter, if you are gonna refurbish everything anyways?)
True. Plenty of crappy properties all over the place.