1. It's not necessarily "nicknameish" sounding to me, but I would rather use it as a nn or mn than a fn. It's cutesy and childish, and wouldn't fit an adult as well.
2. If that's what you want to do, it would be fine. I think it's adorable.
3. I don't. :[
4. No.
Daisy is best as it is, imo. Daisie would be tolerable, though.
5.
Daisy Matilda would be lovely, I think. I personally would use
Daisy as the mn;
Evangeline Daisy,
Eleanora Daisy,
Juliana Daisy,
Annabelle Daisy, etc. What about
Daisy Catherine,
Daisy Susannah,
Daisy Francesca,
Daisy Natasha,
Daisy Gisele,
Daisy Mariah,
Daisy Hermione?
Daisy Elsa Mei is cute.
6. I think of an adorable little girl or an eccentric, lovable grandmother. It does sound unprofessional, but not too terribly so; that's why I would prefer it as a mn and nn.