You have an absolute right to defend yourself at a preliminary hearing, but in my professional and personal opinion, you are making a terrible mistake by representing yourself in a criminal proceeding -- representing yourself at a preliminary hearing is just not a good idea.
If you do decide to get an attorney after the perlim, whatever defense you attorney you hire is not going to be happy -- that I assure you. At the prelim, get a public defender appointed and stay out of the way I guarantee that even the most burned-out unhelpful public defender will still do a much better job than you would on your own.
I appreciate your willingness to take on the system yourself, but with all due respect, you're making a huge mistake, even if it's just through the preliminary hearing. Your question suggests your unfamiliarity with procedure and tactics that can have serious consequences against you.
The burden of proof at a preliminary hearing is quite low - it's a "probable cause" standard. Yes, you have the right to represent yourself at the preliminary hearing - and all the way through trial if you so choose. Because the burden of proof is so low, going to a prelim is an almost certainty you're headed to trial, so a prelim isn't just a fun little thing to try yourself, then get an attorney when it gets serious. It's already serious.
There may be tactical reasons to opt not to cross examine a witness at any hearing, but that would be determined by the case and the evidence. If there was a glaring lack of proof of any particular element of the charge, then choosing to not ask questions and arguing against being held for trial may be a tactic. Of course, getting witnesses locked into statements under oath is another important goal at a preliminary hearing. You can also be setting up defenses for trial if a trial is inevitable. There are motions to dismiss the information under Penal Code section 995 based on what happens at the preliminary hearing, but it's only based on what happens at prelim, so doing the hearing well matters. I've had cases where I asked very specific questions at the preliminary hearing in order to set my client up for the best outcome at trial. I've also asked questions designed to exploit what I thought were weaknesses in the case that lead to the dismissal of all charges on a motion later.
You may want to consult with an attorney BEFORE your preliminary hearing to discuss this in person before you commit to something that you can't undo. You're facing felony charges that carry the possibility of state prison time. This isn't a DIY situation. You're going against a prosecutor who does have formal legal training and is hell-bent on convicting you.
My strongest suggestion: Level the playing field and get representation.