unemployment: can they deny you if you dont accept a demotion?

I live in the state of Oregon. I have recently been able to see the papers that my former employer sent to the employment department. They had me sign what I was told was a termination paper and all it said was "performance", after I left they apparently circled "no" where it said "is this a termination?" and where it said "have any warnings been given?" and she put "yes, verbal and written", which is a lie and was not marked when I signed their cheezy home made paper. The other thing is she is now claiming I refused 2 positions which is also a lie! She said I could go commission only (which is not possible financially due to their low production overall as a company the last 2 months and i do have proof of this) and she also offered to demote me to a position that has a schedule I can not adhere to due to childcare reasons. Now she is claiming I turned them down when in fact I had asked her if she expected an answer now because I feel I should have a day to think about it and sort things out before I accept a position, and I told her honestly that I didn't know I would want to come back, and her response was "just sign the paper then", I don't see that as turning down work, I see that as she didn't like my honesty so decided to just term me. Can they deny me unemployment in this situation? I feel even if I had declined the positions I had good cause not to accept. Also, I have emails of my asking for dental insurance and the owner responding "I will have decide what to do with her soon with her, she isn't making us money at this point", 2 weeks before I was terminated. I viewed these on a shared computer, and the emails were wide open. Can I use this as proof? or would I risk getting in trouble? Is it technically considered my former employers property?
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Yes they can offer you a job that pays way less as long as they offer you a job clears them of any criminal lawsuits. been there. With me no job was offered which made it wide open for a lawsuit.You should talk to an Attorney that specializes in this. it is very hard anymore to convict Businesses as it has gotten so very common,juries have become hardened.
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