FK constraints add a negligible amount of space, if any. The indexes they require do, certainly, but presumably you're already doing joins on those FKs, so they should already be indexed.
Junction tables are how you represent M:N relationships. If you don't have them, you're either storing multiple values in an array (which, depending on your POV, may or may not violate 1NF), or you have a denormalized wide table with multiple attributes, some of which are almost certainly NULL.
Also, these all serve to prevent various forms of data anomalies. Databases must be correct above all else; if they're fast but wrong, they're useless.