@EnderShadowz, welcome to the community!
Right now, you can't change whether a Xenon is a repeater or an endpoint... it is both and can't be changed. If the Xenon is sleeping, it can't relay mesh packets. If the Xenon is awake, it has full mesh functionality but consumes more power. In the future you might be able to designate a role but for now, the mesh functionality is pretty basic. To estimate your battery run time you need to know what the capacity of the battery is and the average current draw of your circuit. Or you can work backwards: if you know the desired run time and the average current draw, you can calculate the battery size to accomplish the run time. There are some power draw measurements for the Xenon posted here in the community but I don't believe that has made it to official Particle documentation yet. The power consumption of a mesh device is only one part of the equation; you also need to know what the sensors and other external circuity will draw. @Rftop has done a lot of battery/solar run-time testing and current measurements and may be able to comment further. See his posts:
Currently, there can only be 10 nodes on a Mesh network including the gateway. The larger networks are future functionality that is being worked on. How large is large?
What would your "receiver" do? In a mesh network, you have the gateway (that handles internet communication) and then nodes or endpoints (for now only Xenons that gather data and publish to the mesh or directly to the cloud). A gateway needs to be always on in order for a node to publish direct to the cloud. A gateway may draw too much power to remain on battery indefinitely without a solar recharge or some other solution.
How long is long? What type of batteries are you using? What temps will they batts be subjected to? What are your recharging options? Too many additional questions to make recommendation on vague requirements.
It applies to both... there is a very low power mode that draws something like 10uA but there are a bunch of caveats. You have to consider the selection of all of your external components to make sure their quiescent current consumption doesn't adversly affect the overall system. (i.e. if you have a LDO voltage regulator that burns 10mA at idle, the lowest sleep mode of the mesh device desn't really matter since the LDO will be orders of magnitude higher.) I think you need to state your exact use case before delving into which sleep modes are best.
See @rickkas7's range testing here: