Imma try to bring this back on topic, and I haven't heard the oboe addressed well, yet.
Range REALLY affects the oboe's timbre, as it does almost any wind instrument, but I feel like the oboe is especially affected.
Oboe does not play a true pianissimo below about a low D. We try our best but the tone down in the lowest register requires a lot of air and pinching the airflow, an important techniques to produce a soft dynamic since changing air speed does crazy things to tuning, will result in the note not speaking at all. Be careful when writing for the oboe in a soft passage. For me as a general rule, higher notes are easier to control softly. I would much rather be playing a pp high G (like, double high G) than a p low Bb.
The oboe has an insane number of register breaks. C-Db inside the treble clef staff transitions from low register to half-hole (the first register key is not pressed down, instead the left hand's pointer finger slides to half-open that key). Eb (D#) to E above that transitions to the first register key. It's a break that is not difficult, mostly because we practice it all the time, but it does make rapid alternation between, say D# to E, difficult. In fact, that D# to E transition is one of the most difficult half-steps on the instrument until you get up above high C.
G# to A (first ledger line) switches to the second register key (Note, the switch happens from G to Ab on english horn, which is the only fingering difference I know of between the two instruments, though I haven't played english horn much at all). This is also not usually something to worry about, but again rapid transition between G# and A are not fun. It's a trill that's never really in tune. I would never write it.
High C to Db is about equivalent to the same break on a clarinet. Meaning, try not to overdo it.
High F to high F# is ANOTHER break, and not a fun one at all.
Really high notes on the oboe-more than two octaves above middle C (which we call "low" C btw)
Yes, it's perfectly fine to write for oboe above high E. I just graduated high school and I can reliably play a high G, and a good professional can probably reliably hit a high A. I've seen fingerings for Db above that (but please don't get any ideas unless, say, you personally know Eugene Izotov :toothygrin: ). Tuning might be an issue but the player can figure that out.
Now, just so you know, the fingerings above high C royally suck. They're really complicated and a half-step slur could necessitate the movement of four or five fingers, or use of alternate fingerings that are almost certainly out of tune (exceptions: High Db-D, high E-F, which only move one finger). DO NOT write extended sixteenth note passages above high D. Only someone like John Mack could play it and sound halfway decent. Endurance/stamina is really a problem in this register as well; I wouldn't keep your oboist there for very long.
Endurance/stamina
I feel like an oboist has less endurance than most wind instruments. This is simply my personal experience, from "losing my embrochure" in band rehearsal before my peers, or playing Mozart's Concerto and knowing that I have all the technique down if I can just sustain my air and embrochure through the entire movement (I'm still working on some technique in the 3rd movement). Try not to keep us above the treble clef staff for forever, although we can sustain it for a good while. Please don't keep us in the highest register for very long; it requires a lot of control and stamina to sustain those tones for very long at all.
To get a feel for the endurance of a good oboist, look at the first movement of Mozart's concerto (there are public domain copies floating around the web, and I even have one on my computer :toothygrin: ). Notice where Mozart gives the soloist a break, and try not to write passages of continuous playing for much longer than that.
Trills/alternations not to write: Low Bb to B. This is just impossible. It's a really awkward slide of the left pinky. A higher Bb to B is possible, BUT it's also an awkward hand position, so add a rest at the end, not ornaments. G# (Ab) to A is possible but not very well in tune. Low C to low Db trill is supposed to be possible with an extra low C key but it requires an awkward finger position on a key that usually has a GIANT hole in it. I still can't reach the key without partially uncovering the hole (and then nothing speaks!). Repeated A to C or G to Bb is annoying. That's about it.
A final interesting note that's vital for any general music teacher working with an ensemble that contains oboists: The double reeds are the ONLY wind instruments that DO NOT have any sort of tuning mechanism to physically adjust on their instrument. The oboe is designed to be played with all body pieces, and the reed, pushed all the way in. Never tell an oboist to adjust the position of their reed. They have to adjust their embrochure or get a better reed.