1. If your database is fairly small, a dump certainly makes sense. However, if your database is huge (> XXX GB), a dump might not be feasible anymore and different means can make sense such as WAL archiving. You also have to keep in mind that a dump only provides a snapshot of data—it does not provide you with point-in-time recovery. Therefore, the dump is more of an additional tool and not a replacement for WAL archiving.
2. A compressed dump is usually around 10 times faster than the PostgreSQL database that you have saved. The reason is that the database has to store the content of an index while the backup only contains definitions. This makes a huge difference in terms of space consumption. On top of that, PostgreSQL has to store additional metadata such as tuple headers and so on, which also needs space.
3. Yes, it is definitely necessary to do that.
4. Yes. If...