As for OM, I am not sure whether your Math background is good enough. If not, you would probably have to spend more than 3 years to improve your mathematical competency during your PhD study. OM emphasizes optimization and analytical modeling. Survey methodology is not widely used in the area.
If you want to do modeling. Stochastic Process and Real Analysis is preferred background. Some Micro background also helps.
Retake GRE/GMAT. It is not hard to get more than 90%.
Internship is not necessary. Also, I don't know there is "conference paper" for OM area. Are you talking about conference presentation? Well, presentation is good but not solid as publication (MS, OR, POM, MSOM, etc...).
For acceptance rate, I know this year is very tough for all areas. In OM, I talked to some professors in 5 schools recently. The acceptance rate was 1 in 30+ for one school, but 1 in 40+ for other 4. However, before this year, the rate should be around 1 in 25. So, apply more schools if possible.