F2cA means it moves/captures on 1st sq or moves/captures on 2nd square if 1st sq is empty or captures on 2nd sq when 1st sq is occupied. It cannot move on 2nd square if both 1st and 2nd are empty. Is that what you want? IMO, this is too irregular. It is your game, sure, but I would recommend to have FA, i.e. the Elephant (that you may call as you want) to simplify.
Chancellor: RN
Falconer: my apologies, saying this one in Betza's is not so easy. HG knows.
General: BnDD
Lancer: DY as on the diagram. HDY as suggested by Aurelian.
Lioneer: not very easy again. Seems to me that it is similar to the Warlock of HG's Elven Chess. Then, it is KNADmabKcaKcabK.
Nightrider:NN
Pawn: ifmW4fmWfcF
Prince: FN
Princess: BN
Sergeant: fFfW3smW
Soldier: ifmW4fmWsmWfcF
Spy: I don't know if you accept that it moves to 2nd sq if 1st is occupied? If you don't, then, W2N
Tank: not simple again. RjR may work maybe.
Wait for confirmation though, they are better experts than me on this site.
Consider that you can test yourself these Betza's notation to check if it is what you want with HG's Play-test applet:
Archer: I don't understand what mF2crM is.
F2cA means it moves/captures on 1st sq or moves/captures on 2nd square if 1st sq is empty or captures on 2nd sq when 1st sq is occupied. It cannot move on 2nd square if both 1st and 2nd are empty. Is that what you want? IMO, this is too irregular. It is your game, sure, but I would recommend to have FA, i.e. the Elephant (that you may call as you want) to simplify.
Chancellor: RN
Falconer: my apologies, saying this one in Betza's is not so easy. HG knows.
General: BnDD
Lancer: DY as on the diagram. HDY as suggested by Aurelian.
Lioneer: not very easy again. Seems to me that it is similar to the Warlock of HG's Elven Chess. Then, it is KNADmabKcaKcabK.
Nightrider:NN
Pawn: ifmW4fmWfcF
Prince: FN
Princess: BN
Sergeant: fFfW3smW
Soldier: ifmW4fmWsmWfcF
Spy: I don't know if you accept that it moves to 2nd sq if 1st is occupied? If you don't, then, W2N
Tank: not simple again. RjR may work maybe.
Wait for confirmation though, they are better experts than me on this site.
Consider that you can test yourself these Betza's notation to check if it is what you want with HG's Play-test applet:
https://www.chessvariants.com/page/MSplay-test-applet-for-chess-variants