fundamentals of Transmitter Chain design

I have a chipcon chispet that provides +3dBm Tx power out. I am required to have +13dBm out. I found a PA ic that has favorable specs and I need to determine if some sort of bpf or hpf is "absolutely" required. In other words can i live without the filter in this design?

Only an RF system analysis can give you the answer.
BPF before PA's generally are used to eliminate the broadband noise, when LPF are used to suppress the spurious and harmonics.
I don't know, just place the PA in the circuit and see if you break any specifications.

This particular transceiver chipset internally has no filtering.
Just mixer,amplifier,antenna

I just want to know if my design is fundamentally flawed if i just integrate a PA with the transceiver soc and let the rx chain design be good enough to deal with selecting wanted signal from unwanted signal.

Considering that the antenna is tuned to perform in a certain freq range, doesnt that help with supressing mixer spurs and amplifier im products?