Yes mayo can be used in place of eggs in meatloaf.
Mayonnaise contains eggs which make it a binding agent for the meatloaf so if you have no eggs but have mayonnaise you can use the mayonnaise instead of eggs when making the meatloaf.
Cooking meatloaf in the oven at 375 F takes between 1 hour and 1 hour and 30 minutes depending on the size of meatloaf you're cooking.
If you have a meat thermometer you can use the meat thermometer to tell when the meatloaf is done and ready to serve.
When you insert a meat thermometer into the center of the meatloaf and the internal temperature reaches 165 F degrees then the meatloaf is done and fully cooked.
If you notice any pink color to the meatloaf then it needs cooked longer until there is no pink or raw meat.
For me when I cook a meatloaf it takes 1 hour and 25 minutes for the meatloaf to be fully cooked.