All you can do is deny that you touched her property.To your knowledge did she move anything out of storage after you asked her to.

The more I got denied, the more I wanted a property!

Can I deny them for this reason even though they said non-smoking? 

Anyone is welcome to confirm or deny THOSE numbers.

They would not be directly denying my solar panel installation but the reality is, I cannot install it with a wood shake roof. 

@Sam LLoyd if you are getting too many denied applications, it means you are not doing a good enough job of prescreening.

@Johnathan Norman      I am sorry Jonhathan , I have had to deny your request to rent my house due to your criminal record .

Should I deny them?

I strongly recommend that you find a Central Jersey VA loan specialist, confirm/deny anything I have mentioned here and get a firm understanding of minimum timelines between VA loans too.  

I'll second what @Hadar Orkibi said about not applying for anything that would affect your credit if planning to take a bank loan or similar.I went on a rewards credit card rampage last year and signed up and was approved for 3 of them and finally denied on my fourth attempt.