Welcome, it's always good to have a new Bari player join the fold.
The D thing may well just be the horn trying to sound the lower octave. Bari needs a bit more finesse than most folks think. Try starting on second line G, and slur up to D. Don't use the octave key. Just hear the pitch before you play it. It will take a few tries. And it won't happen all that regularly very quickly. You need to voice the pitch just as much on the Big Horn as you do on flute. Don't sweat it too much. We all have growing pains. And not everyone hurts the same way.Might have the horn checked over though, the lower octave pip may not be working right.
Change the reed when it gets chipped, it splits, looks like it's been rubbed with dirt, or starts playing "fuzzy". When in doubt, throw it out. My wallet dislikes the idea, but my sound thanks me for it. Take care of them, and I usually get @ 20 good playing hours out of one.
The embouchure is really fairly simple. Keep the corners firm enough that air doesn't leak out the sides. Make sure to take in about an inch and a quarter or more of the mouthpiece. It's not too much until it stops playing. And have just enough lower lip rolled over the teeth to make a nice pad for them. Never think about pressure or tightness. Just give the reed enough support to allow it to sing.
Play it like you mean it. Bari ain't for the shy. Unless you are "Bari-ing" the lead alto and/or bass 'bone it's not too much.
The family called it the Dead Moose back in the Day. Still do now and then. Just try to play bigger than any flock of geese could ever be, and keep the ears going. The sound will mature in time.
Start digging into Real Bari Players.
Gerry Mulligan. the Granddaddy of us all..
Tower of Power. Doc's sound will wit you like a brick wall.
The Airmen of Note. Doug makes the Old Girl sing real nice.
Don't hesitate to ask if I can help more. Always have time for another Bari Player.
Welcome to the Family!
Bari is my first love, everything else is just a mistress.