Your carpet will look and feel better with underlay, and will last longer. But it's not essential - it's up to you. Pay you money & take your choice.
I'd agree with the welsh librarian on grippers; proper grippers are well worth it, and they aren't expensive if you buy & fit them yourself*. They'll keep the carpet in place, allow better fitting and - if it's properly fitted - stop it getting bumps in.
* Easy to do, basically all you need is a hacksaw, hammer and gloves. Instructions can be found on the 'net.