C2H6N (I'm going to assume as NITROGEN) - Cannot exist, as there would be too many hydrogens if all the electrons formed a covalent bond with another atom. You would think that you can make a atom like [CH3-CH=NH2](1+) where 1+ is the overall charge on the molecule (One of the hydrogens form a dative covalent bond with the lone pair on the nitrogen), but it is more likely that the C=N double bond will break, as it is more unstable. Also, in order for a ion to be made, high pressures will be needed, so (assuming you're in room temperature and pressure) it won't exist. Woo. essay, haha.
C3H5Br2 - Is unlikely to exist, because a carbocation (a positive carbon in a organic molecule) would exist. So it'll probably exist for a fraction of a second before a nucleophile (electron pair donator) will attack it and for a dative covalent bond with it, changing the structure.
I think it's right, but I'm only in A2 Chemistry, so hope this helped! =]
These molecules would be charged but you haven't specified what the charges are.
C2H6N+ wouldn't exist as you'd never be able to remove H- from dimethylamine. You could remove H+ though with a very strong base like butyl lithium. So C2H6N- (negative charge on nitrogen) can exist. You can even buy this from sigma aldrich as as the lithium salt - LiN(CH3)2. This molecule will be very reactive though as it really really wants to pick up a proton so it will exist as long as there isn't any other molecule around with even a slightly acidic proton.
C3H5Br2+ is too unstable. Maybe as a very short lived SN1 intermediate but you'd never isolate it. As for C3H5Br2- (assuming it's CH3C(-)HCHBr2), the free electron pair on carbon would spontaneously kick into the adjacent C-C bond to eliminate a bromide and give CH3CH=CHBr.