See this thread from Autodesk Eagle Support Forum.
It is a feature called "Auto Loop Removal" that they added in eagle V8.xx. You can enable or disable this feature when routing by simply clicking the loop removal off or on icons on the toolbar when the route tool is selected:
It is probably fine for this application, I've done this a few times. The few nH's of inductance and mΩ's of resistance that the vias add will not affect the rise times of the reset line for most parts.
If you're worried about the rise times in nanoseconds or if the RST line is impedance controlled, then you might have to worry about adding vias, the most ...
Eagle doesn't have a concept of specific purposes for copper layers beyond top and bottom being used for component placement.
Your layer string is fine for what you need. (1+2*15+16) creates a four-layer board with no blind or buried vias.
You will get in Eagle the four routing layers, 1, 2, 15, and 16, which are all simply copper layers that you can use ...
For the clearence between the pad and the ground plane, go to Design Rules -> Supply -> Thermal Isolation.
To change the thickness of the connection between the pad and the plane, change the thickness of the polygon outline.
Another reason for the vias around the mounting hole is wave soldering. When wave soldering solder covers all unmasked copper and therefore the whole mounting hole would be covered with solder. Manufacturers usually mask those holes with some tape manually which costs money. This way you have the electrical connection thanks to those vias that can be ...