yes it is possible to send downlink without transmitting uplink first.
Either you configure class B for your device, then you can define receive windows in a specific interval. Or you configure class C. Then your device opens the receive window as long as it transmits an uplink packet. But the device is not in sleep mode which costs much of energy.
What do you mean? You are not able to receive the downlink from the server?
This can due to various problems.
Maybe your node can not process the SF of the downlink packet. In ABP, you can define e.g. the SF of RX2.
Use this as generic calculator to calculate battery life and capacity:
C = Battery capacity (mAh)
BL= Battery life (years)
Is = Current when device is in sleep mode (mA)
Itx = Current when device is in transmit mode (mA)
Irx = Current when device is in Receive mode (mA)
Imeas = Current when device is in measurement mode (mA) [it depends on technology used and application]
Ttx = Amount of time that device is in Transmit (TX) mode (ms)
Trx = Amount of time that device is in Receive (RX) mode (ms)
Tmeas = Amount of time that device is in measurement mode (ms) [depends on technology used and application]
Ta = Amount of time that device is active (ms)
Ta = Ttx+ Trx +Tmeas
U = Usable capacity after taking into account self-discharge (%)
N = Number of times the device will be active per day
cU = Capacity after taking into account discharge rate (mAh) = C*(U/100)
T = Milliseconds per hour = 3600000
cA = Active capacity usage per day = N*(TtxItx + TrxIrx + TmeasImeas)
cS = Sleep capacity usage per day = Is( 24-((Ttx + Trx + Tmeas)*N/T) )
cT = Total capacity consumed per day = cA+cS
Battery Life (days) = (cU/cT)/24
Battery Life (years) = days/365.24
P.S. for class C endnoes highly recommended to use the external power.