What is this type diode & transistor?
2) Yes, that is almost certainly a good substitution, the parts are nearly identical.

https://www.infineon.com/dgdl/irfr5505pbf.pdf?fileId=5546d462533600a4015356358535210f
https://www.infineon.com/dgdl/irf9z34nspbf.pdf?fileId=5546d462533600a40153561228de1de0

If you suspect that the gate isn't driven hard, also look at the Vds I-V curves. The replacement is more sensitive, this is good.