1: Not sure if there is a NEXT kind of function in MyDMX, it's not something I've needed, but I can see the need for it. My DMX doesn't operate with true chases. You have to make your own by chaining scenes or building complex multi-step scenes or BOTH.
You can always duplicate the scene to make it a "combination scene" but sometimes adding elements can be very difficult, especially if you're adding moving heads or doing transitional color changes
2: No. You can only run 1 scene at a time. It is an intentional limitation of MyDMX. This isn't meant to be a negative about MyDMX. To get the type of features you're looking for, you simply must step up to higher end software, regardless of who makes it.
If you want to overlay scenes, you'll need to step up to Compu Live or Compu Show, which are both excellent products.