In the same order you asked:
Any continuous piece of DNA that is obtained by reliably overlapping shorter reads can be considered a contig. That means that a 200bp of continuous DNA would be a contig, but it would take a much longer piece to call it a scaffold. I don't know if there is a formal cutoff when a config becomes a scaffold, but let's just say that a scaffold is definitely a contig, while the reverse is not necessarily true.
Not sure I understand this question. If you already have a fully assembled chromosome and scaffold/contigs are not in it, that would mean they are potentially parts of a different chromosome. If you are talking about a chromosome from a reference assembly, then most scaffolds/contigs should be in it assuming an assembly without contamination.
It won't harm the alignment to reference genome whether you remove them or not, though the final aligned fraction will be smaller if these scaffolds/contigs have no matches in the reference.