Why I need Redis if there is already memcachedb?

Memcachedb is basically memcached done persistent. Redis is a different evolution path in the key-value DBs, the idea is that the main advantages of key-value DBs are retained even without a so severe loss of comfort of plain key-value DBs. So Redis offers more features:

Can I backup a Redis DB while the server is working?

Yes you can. When Redis saves the DB it actually creates a temp file, then rename(2) that temp file name to the destination file name. So even while the server is working it is safe to save the database file just with the cp unix command. Btw we are working on transparent replication.

What's the Redis memory footprint?

1 Million keys with the key being the natural numbers from 0 to 999999 and the string "Hello World" as value use 100MB on my Intel macbook (32bit). I don't have numbers to compare the memory usage with other systems like memcached, I'll be glad if someone can provide this numbers.

What Redis means actually?

Redis means two things: