To be honest, you could in all likelihood get that mostly all on in the one go which might be a bit easier if you're doing it to yourself. As foam is porous it both draws in the glue and helps let it dry by continuing to keep air in contact with the (air drying) prosaide. As long as the glue is still wet, you'll be able to reposition it before it grabs.
If it was me ( disclaimer - I do this all day every day for work ), I'd first clean my nose. Noses are oily so this step will definitely help. I'd then load enough glue to make the surface wet into the piece (not enough so it runs all over the place) with a q tip. Keep the glue at least a good 10mm from the edge. Then get this situated on your face where it wants to sit and is comfortable. Hold it in position until you can feel that it's grabbed. Doing it this way rather than letting the prosaide dry first lets you have some repositioning time.
Once the weight of the piece is held by the glue, you can go about doing your edges. This will be tricky as it's in the middle of your face and you'll need to cross over your eyes as you work round the edge. Use a damp rather than sopping wet qtip and work from the glued section outwards, being careful not to fold your edges over. You can seperate the edge of this happens but that's easiest to do with 96/99% alcohol so wouldn't be overly pleasant round your eyes. (96 is far less fumey).
If the above is your piece, the main area you'll have trouble with is the underside of the nose where it meets your top lip. For this section, I'd probably get most of the nose on and secure and then apply glue to both your face where it meets and the piece. Let that dry and then carefully (making sure it's in the right place) contact the two surfaces together. That'll get you a better bond than just gluing as you go.
If the piece is made for a your face then the edges should be pretty good. If not and it's more generic, offer the nose up before you even open the glue and take note of any areas that it doesn't quite fit. When you then come to glue these down later you'll have an idea of which bits might need a gentle tug to get them to lie down nicely. You'll have more luck hiding tricky edges in the corner of the nose and underneath than you will smack in the middle of your face around the top edge.
To finish foam edges I often make Dick Smith's edger, comprised of 99% alcohol and spirit gum. As you're allergic I'd skip this and stipple your edges over with prosaide on a sponge (you need an open cell sponge like you'd wash a baby with, not a foam latex wedge as this won't work so well). If there's a small ledge you can either thicken some prosaide ahead of time like udog said or you can buy a small pot of prosaide cream when you're buying your glue. In all likelihood this is enough to disguise your edge.
If none of this gives you the finish you want, the nuclear option is making some Bondo / cabopatch. This is a filler made of prosaide and fumed silica. Fumed silica is very much not something you want to breath in in its powder form (much like asbestos), however it's inert once suspended in a liquid. If you do choose to do this then you should be wearing a respirator and in an ideal world, do it outside with everything you're using inside a bin bag to avoid throwing it everywhere.
Once you're glued, apply some translucent powder (I like RCMA powder, others exist) to your glue to stop it being tacky and allow you to move your nose without it sticking to itself.
Colouring can be done a number of ways. Generally I'd start a raw foam paint job with pax paint. Pax paint is prosaide mixed with acrylic paint that can be stippled on with some more of that sponge from earlier. Traditionally it's made from liquitex paint but any non-toxic acrylic paint will work. Mix in some colour to your glue untill you achieve a density slightly more like cream than milk. It dries darker than it looks when wet so bear that in mind. You can do this before you apply the nose but make sure that you leave your edges clean as the paint will sink in and make them less malleable and prone to deformation if not which will hamper your application. If you do prepaint - powder when it's dry before you touch it. Same powder as above. If you're painting it on your face, powder also after this step to stop it being tacky.
There are a number of paints you can use to tie in the rest of your nose to your face. Industry standard is alcohol activated colours like skin illustrator or reel color (other brands exist) but these are quite expensive for a one-off however so you might be better off with some rubber mask grease paint (rmgp). Kryolan sell various 6 shade pallets one of which would likely suit (other brands, also exist) This you can apply with a brush or a latex wedge, building up colour to match your own skin tone. This will need powdering when you're done to set the makeup.
Noses are tricky as they're smack in the middle of your face so any irregularities are easier to see. You'll also spend so long looking at yours in the mirror that youll likely be overly critical. As long as the general tone is there and it looks like a nose, you'll probably be fine and dandy.
