1.1 You will need some kind of periodic boundary condition to identify your hbonds correctly in most cases. Hbonds will automatically take PBCs into account if present. Follow up question what exactly do you mean by "wrapped" vs "unwrapped " in this context?
1.2 You can add your periodic boundaries by specifiying the box in MDAnalysis format and assigning it to ts.dimensions IF you know what it is. For example:
for ts in u.trajectory:
mybox = np.asarray([A, B, C, alpha, beta, gamma]) # how do you know A,B,C, ... ?
ts.dimensions = mybox
My main question is how do you know what your PBCs are if they are not in your XYZ file or another format. It may be easier to convert to some other file format. Perhaps you can give me clearer idea of your workflow.