How to pay for or avoid publishing cost without research funding and without limiting journal choice
Can the cost be shared among co-authors? Is it common for the first author to ask money to the co-authors to pay for the publishing costs? 


It is not common to share the fee of one publication. However it is common to ask for a collaborator to pay the full fee if he has a funded project and then you pay for other publication in the future. 


  Are there certain journals that might waive the publication fee given the financial circumstances?


Yes. I am from a country which suffered several cuts in science due to the 2008 crisis and my research center was left without funding for several years. Due to the lack of fundings my supervisor started to ask for fee waiver and he got several waivers from Open Access journals, such as: PlosOne, Plos Computational Biology, Nature Scientific Reports, etc.

In the PLOS journals he is used to get 50% of discount and in the Scientific Reports he got 100%. The Sci.Rep. staff asked for the research center budget in order to deliberate if they would give a discount or not.

Usually you can find the waiver policy in the website of each journal.