I advice you to dechorionate embryos manually with forcepts. Usually, I fix embryos (in PFA) and then I stock them in MeOH. For Immuno, I make 3/5 wash in PBT (PBS 1X + triton) and then I dechorionate them, before blocking.
Yes. After PFA fixation, wash your embryos with PBS 1x + triton (0,1 to 0.5) at least 4 times (1 quick wash, 1 each 10min x 3) in order to eliminate PFA (it is toxic). Than, you can decorionate embryos in a dish. Once decorionated, you could:
1) stock your embyos in Methanol MeOH (1 wash MeOH/PBT 1:1 Vol; 2/3 wash MeOH 100% RT, each for 2 min, then stock embryos in MeOH 100% at -20°C)
2) Put your embryos in an eppendorf and start your Immunostaining (1or 2 wash PBT, than blocking solution without 1st antibod, than blocking solution with antibody etc...).
For early stages (up to early somitogenesis) I usually decorionate after PFA fixation (it avoid problems with the yolk), from 24hpf I usually decorionate prior to PFA.