1) (repeat of ag) Battery should be bypassed.
2) R1 is good for HFE at minimum, but what is the bias point for HFE at maximum? With no max HFE specified for BF199, I would use a bypassed emitter resistor and a fixed base bias point, but that's just me. Do you intend class A or B?
3) With a little calculation, you should be able to determine a fixed value for C3. What do you expect will be your nominal setting for C4?
4) There is no base bias on U2. It won't ever conduct.
5) R3 should be bypassed unless you really want it to soak up your RF and lower your output Q.
6) What are the values and characteristics of L2 and L3?
7) I would like to see the typical reactance (R, +j, -j) that you expect, at the operating frequency, in the output pi filter so I don't have to re-do your math. You did do the math,, correct?