Mitch, you need a package policy that covers all your properties. The policy should include coverage for each property, as well as liability for each location as well. The product I'm most familiar with provides your requested property limit for each location, as well as a $1MM per occurrence / $2MM general aggregate limit for each separate location as well. The product has a builders risk or rehab component built into it. I'd suggest getting something along these lines for sure, and making sure the product can quickly and easily add and remove properties as you do your work. This is even more important if you plan to work multiple fix-&-flips at a time.
Errors and Omissions is important to protect you when you fail to manage your LLC professionally. However, if you willfully neglect to do what's required by law, you likely won't find coverage under that policy.
You would certainly want protection for yourself if you are hurt and out of pocket for a number of weeks or months, but not sure what options you have outside of the standard health/medical insurance for yourself.
However, when/if you hire a contractor to do your remodel work, I certainly suggest that you confirm that they have workers comp and general liability coverage in place, and with decent limits (most have at least $1MM in GL coverage). WC depends on their number of employees and state WC laws, but most states require WC coverage for employers with 3 or more employees. If the contractor's carrier will add your LLC as an additional insured during the course of their work, then that's even better. Please note that listing your LLC as a certificate holder is "NOT" the same as listing your LLC as an additional insured. If the contractor's carrier is willing to add your LLC as an additional insured, then that just better protects you if anything happens.
If the contractor is doing any significant structural work, or adding on to the existing home/building, then I'd certainly discuss them having their own builders risk policy due to the size and scope of the work they're doing.
Hope this helps sir!