I did the SHR solo this year in mid July. For pictures and info on my trip, you can go to the page on my website below. I'll be adding more to this as time allows, as I just got back in town for the season and am still playing catch-up.
Based on my SHR hike, as well as early season PCT and JMT hikes, here are my thoughts on your specific inquiries:
1: S>N is easier for a couple reasons. First, the pattern of the major forces that formed the Sierra (glaciation for example) tends to result in S>N oriented passes that are steeper on the North side, and W>E oriented passes that are steeper on the East. Hiking S>N tends to result in descending the steeper side of most of the passes. This is advantageuous because when down-climbing steep or technical terrain you have a greater line of sight and it becomes easier to pick out a good line. Further, I clearly recall (when looking back South) that several of the passes would be more difficult to identify vs. hiking North.
N>S hiking has the advantage of shorter resupply distances for the first half of the route, but personally, I would unquestionably consider S>N a 'better' way to hike the route.
2. I carried fixed length poles (BPL Stix) and they were never a nuisance. I would consider poles TOTALLY essential on the SHR. I can't count the number of times they saved my butt from slipping, they were great to have on snow, the countless STEEP climbs, for vaulting streams, for stability on steep, unstable scree, and for big talus- since I could use them to sort of "vault" gaps I would otherwise have to scramble down and up. If I didn't have poles I would have trashed my knees. The SHR is steep almost all the time and the talus sometimes requires taking big up/down steps (like thigh-high) all the time which is hard on knees.
3. I dunno. I carried a bear can and hated it with a passion. Next time I might risk the fine. I think the NPS policies are skewed towards people who don't know how to behave in bear country, and assume most high use occurs in bear habitat... which is fair. Still, it's frustrating. I hate bear cans, and if you know what you are doing, I don't think they are necessary, particularly on the SHR which is generally in very low use areas or not in bear habitat. Just my $0.02.
4. I carried a one liter soda bottle. I didn't treat any water, and on 90% of the route I just grabbed a sip or two at a time. Water is EVERYWHERE. There is one @10 mile dry stretch on Mammoth Crest South of Red's Meadow, but this is the standout dry section, nothing else was nearly as long.
5. 'Early season' (in the way you mean it) can be a pretty flexible term: In early season in a dry year, there can be less snow than late season in a wet one... I didn't carry crampons, and even on steeper snow I never would have used them. If you run into hard snow you could always wait a few hours for it to soften up, which the snowpack does pretty reliably in the Sierra. I did carry an ice axe and probably would again.
6. I think it would depend on the terrain you are most comfortable on. There were definitely occasions where I was wishing for snow because the talus SUCKED... there is a LOT of talus on the SHR. But while faster, snow can be just as, or more treacherous, particularly if it is rotten with air pockets and undercut edges. I would guess that if you hiked early in the season, what time you would gain by walking on snow over the talus would mostly be offset by having to be more careful on the steeper snowfields.
7. I would doubt it, unless you were very early in the season or if it was a very wet year. The SHR has a lot of high terrain, but lower stuff is never that far away and the high elevation/North facing sections susceptible to heavier snowpack are not sustained. You might pull a long day or two, but I would be surprised if you ever HAD to camp on snow.
8. I seriously doubt it. I've been in the Sierra in August in dry years, and there's still little snow patches and springs all over the darn place. You might carry a liter instead of a few sips like earlier in the season, but provided you keep moving, I seriously doubt you would encounter any real water issues.
9. Hiking solo I usually hike in the high 20's to low 30's.
Solo on the SHR I averaged in the high teens/low 20's. SHR miles can be VERY slow and there are tons of steep steep climbs, lots of talus, bouldering, etc. Even if you are comfortable on technical terrain, I would almost certainly anticipate your mileage dropping by a third or more.