"in circuit" always depends because of the surrounding circuitry. I won't say "always yes" or "sometimes". In general, you can.
The correct word to use when a transistor is "turned on", is indeed "turned on", or "in saturation". There is a spec called "Vce (Sat)". It's generally the lowest voltage drop you can get across the CE junction. "forward biased" would mean some amount of conduction, but not necessarily fully on. At least, that's my interpretation. It would mean, you could measure a Vbe across an NPN transistor with a voltmeter in circuit.
PNP's and NPN's just have their polarities reversed, so ~0.7 V across a BE junction of an NPN transistor makes sense, but so does a 0.7 V across the EB junction for a PNP makes sense. Just look at the schematic and follow the arrows. The arrow can be assumed to be the arrow of a diode.