Hello,
To answer your questions:
1) It will be fine as long as you make an affirmative case for why you want to do what you plan to do. That said, work experience should show upward growth and increasing responsibility – plus as much impact, leadership, and achievement as possible. So evaluate your w/e critically in this context, as it will be a factor in how competitive you are.
2) Many successful MBA applicants don’t have formal managerial experience; however, they should have some
leadership experience (formal or informal). If the title is so-so, use the essays, resume, and application form to portray your significant impacts, responsibilities, and achievements. Also, adcoms understand that there are many organizational structures. In a matrix organization, someone may be a major player but have some banal title. Adcoms understand, but it’s up to you to clarify the context and details.
3) Assuming a GMAT of 710 at least, the schools mentioned contain a good range from
reach to on-pars – though Haas might be a pretty high reach. Have you also looked at USC Marshall?