How much / what method of script analysis might you use to prepare for rehearsal?
How much depends on the script. Do you understand the script? Do you have any questions? If so, continue reading, researching and talking with the writer.
There is a big difference between character driven stories and plot driven stories. You'll need to work more with the actors, with deeper characters. It'll also depend on the quality of your actors, where you are as a director and where everyone needs to be for the production.
What rehearsal goals do you have ahead of time?
Once again, it depends on the script and who you're working with.
Directing and acting are very people orientated jobs. Relying upon one rigid process can make you unable to work with particular people.
My goals tend to be to establish trust (both ways), get everyone on the same page, if need be (and time permits) experiment to enhance the characters and/or story. Lay out and practice blocking. The goal is to get the best result you can possibly get with the allocated resources.
What order of 'things' do you do in rehearsal?
This is really a "How long is a piece of string" question. There are so many variables. Budget and time restraints are just some of those.
How much time do you spend discussing the script?
How much time do you have? You cannot go over that amount of time. Do you need more questions answered? No need to continue. It will really depend on the script. A short film is going to be different from a feature film. A deep, multi-layered script with lots of subtext are going to require more discussion than say a no budget, 2 dimensional action flick.
Is it horrendous to run through each scene again and again, while trying different things, or will this bore the actor?
Depends on the context. Is this for your benefit or your actors benefit? If it's for your benefit, it'll probably annoy your talent. You may come across as someone who doesn't know what they want. You know, one of those people without a vision.
If it's because your actors want to experiment, go wild. You may get some great surprises come from it. Once again, it'll depend on the resources available.
Know your stuff. Be adaptable. Be professional. Be prepared (though it doesn't always work out how you want, so you need to know your stuff as well as you can)
Take for instance, last night, I had a shoot pretty much go pear shaped... in this case, pear shaped is a bad thing. About 2 or 3 shots in, the person who was the director of this 3 hour action shoot with stunts, turns to me and says, "I'm not a director. You are. You do it". At that point in time, I was cursing myself, "I really should have paid more attention to what the plan was." I had never directed a stunt shoot before, and here I was, no shot list, no real idea what we were shooting, short on crew, unfamiliar with all the cast and crew except for one actor and less than 3 hours to go. Ideal right? The only option I saw was to ask direct questions and move as fast as possible. With most of the rough cut complete today, it's worse than I hoped, but better than the disaster I expected. Running short on time, I missed a lot of coverage I wanted (that will hurt), and some stunts the producer had hoped to capture. It was still fun and a good experience.
Sometimes you just have to make do with what you have a figure it out.
I'm sorry but these answers probably aren't the answers you're looking for. There's a lot more to do with directing than picking a particular process to use. As I said on that other thread, you do need to find what works best for you.