One thing you need to understand - the Old Master's were realism. Hence why she's probably telling you to paint an blue area blue. That's how it really looks. If you want to use Orange where a shadow is, well, there's a style for that too - but it's NOT Old Master's. Oh and the typical order for painting is *SLIGHT* outline (or if you're advanced enough you can skip this), DARKS, Midtones, HIGHLIGHTS. Landscapes, animals, portraiture, it's that order - Darks, Mids, Highlights.
Now, moving on, I see a few problems with your painting right off the bat. The peaches look good - they don't need to be developed further yet. However, the background is the wrong color, the branch needs to be darker, you have a shit load of leaves to mass in, and the pears are too yellow. Plus, it looks like you're just getting started. The first couple layers will look like shit. That's how it works. You DID get all the white off the canvas, that's good.
background to foreground is good because you can start off with the farthest object, and simply go over it. If you can't see the whole object that's a little different, but it should still work. With still lives, it's best to start with the largest object and go from there. You've got all the objects massed in, so right now I think what you need to do is start slowing down; be careful with your colors, and start looking more at values. Plus that red vase looking thing on the very right is too small.
Plus, like I said, that background needs to have more red, and I think it needs to be darker. For the leaves: Start off making them totally black and get the shapes right (there's a HUGE black mass of leaves and stuff next to the grapes in the painting, but they are MISSING in your reproduction!). Once you have the shapes of the leaves right, you can start BUILDING THEM UP. What I mean by this use using the correct colors, and keep the leaves mostly in shadow.
Also remember that this will take you a while to make it look great. Old Master's stuff isn't basic work. Not by a long shot. Hence "Master's". As for technique, you can lift out highlights with just about anything (I think a good cheese cloth is nice - and it's a VERY common way to lift out midtones and highlights), and clean brushes usually work well for blending. I think you can start using more paint and less "thinner" - whatever you're using for it. Liquin, Linseed oil, or whatever. Also, unless this class is required, and will gravely affect your GPA, or has other consequences, this painting will take some time. I would say don't rush, but if you have a legit reason to do so, well, develop the painting more.
Hope this helps. If not, lemme know.
Doctors heal you, Artists immortalize you.
"Those who can, do. Those who can't, teach" - bullshit.
The usual staples for anatomy: