Be aware that Asuncion in February will be unbearably hot!
You can stay in a 3 stars hotel downtown for 20 dollars a night. I stayed there for one month and found it fairly confortable. You can rent an apartment, everything is negociable there. Your best bet is to find a local, and ask him if he knows somebody who rents one, tipping him for the service. You can find an monthly rental from 600,000 guaranies (150 USD) and up, depending on your negociation skills.
Life is cheaper than in Buenos Aires, but social life is also much more limited. Dont change cash in the streets, you will expose yourself to lots of scams, from false bills to wrong calculations.
My 2 guaranies of advices (that is VERY cheap

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