How to start a grassroots DH race?
Am I correct in thinking (based on your PinkBike comment) that you've never personally participated in a DH race?  I would very highly recommend you compete in a few before trying to put on one of your own.  

There's a ton of things you'll need to think about, and the best way to get a good list is by attending one yourself and looking around with a critical eye.  Off the top of my head, other things you need to prepare


Bathrooms/porta potties
Race bibs
Food/water
Course marshals 
Parking
Prizes

Other suggestions from comments
Insurance - @Daniel R Hicks
Medical support - @Jahaziel
Course preparation @Jahaziel
Race Categories - @Jahaziel


Competing in a race would give you a chance to look at all these things, and how they can be done well/poorly.  It would also give you a chance to speak to the race organizers in person (although they'll likely be quite busy, you may need to wait until the end) and pick their brains.

If going to a different race isn't an option, you might still try to contact organizers and talk to them over the phone.

In response to your specific questions, I know there are websites to handle registration; you might check out http://racesonline.com/, they've done a few races I've been to.  Or you could probably get all the info you need with a Google Drive Form, but that might be a little hard.  On the upshot, it would be free.

As far as timing, there are companies that will rent/come out and operate chip timing equipment (I don't know any off the top of my head), but the budget way to do it is to start two stop watches at exactly the same time in the morning before the race, then send one to the start and one to the finish.  Then you have a person at the top recording the starting time of each bib number, and a person at the bottom recording finishing time.  At the end of the day you go through and subtract all the start times from the finish times, and presto!  This is very cheap, but it's imprecise, and it means you don't get results until the end (unless you have more people with radios communicating times back and forth, which is doable but requires extra hands).

Practice runs seem like they're more or less up to you, and could probably be handled with a chalk board.