My WD was my first self-found character to clear Inferno, back in 1.0.4. I can currently farm MP3 with him pretty quickly with his relatively bad gear, which to me indicates the WD is still the class to beat for self-found progression/farming.
To answer your questions:
1) I have no idea. My WD has had trouble finding a really awesome mojo so I'm using a 2-hander with 300 int and around 200% crit damage, as that has been the best weapon I've found for him.
2) They are excellent, and likely what makes playing a WD so easy. Either the dogs or the Gargantuan can tank enough for you to focus on mowing mobs down. Running both dogs and Gargantuan makes it even easier. With dogs cooldown at just 45 seconds now, you should basically never have no pets out, unless you got really hosed by positioning and something like desecrator.
3) Use it in combination with Spirit Walk offensively. While pets are tanking, Spirit Walk in, drop Soul Harvest, cast some Zombie Bears, run out. If you run Grave Injustice, you can keep this up for a while. Alternately, a lot of people run Soul to Waste just so they don't have to burn Spirit Walk on doing this over and over. I really don't like Soul Harvest, though -- I always forget that I need to refresh it, and I generally feel like I really need it specifically when it's not safe to cast it -- a pack where you might need Spirit Walk defensively, for instance. With that said, the Siphon and Vengeful Spirit runes are a little better in terms of not forcing you to use it offensively -- Siphon is a defensive use in case your tank wall stops holding up, and Vengeful Spirit can trim a lot of mobs on low health that are closing on you at once, while refreshing your stack.
4) Playing self-found with all 5 characters, LoH/LS are a huge problem for me. I've yet to find an item with any of my characters that has good damage as well as LoH. I've done a little better with LS as my DH has a decent LS bow. However, this hasn't really stopped me from progressing -- you just have to be a little more judicious with health globes. (Barb and Monk suffer the most, obviously.) But honestly, the WD playstyle is so safe and almost autopilot at times that you shouldn't have any worries. Between Spirit Walk and Spirit Vessel, you really have no excuse for dying -- if you Spirit Walk out of trouble, chances are you will de-aggro mobs, which gives you a chance to recast pets and go right back to it. And that's assuming your pets even die in the first place. I never really bothered to go for any regen, LS, or LoH with my WD, and he still had no issues clearing 1.0.4 Inferno (something like 300 life after kill and 63 life per second, never running Blood Ritual). Healing Journey is a good alternative to Jaunt if you really feel like being "safe," however, though I always liked Jaunt more because it's more versatile and it's not like health globes are rare or anything.
1.) I personally like 1h+mojo. The bonuses a frog gives are way too good.
2.) Pets are awesome. Go for Gargantuan-Humongoid, my fav.
3.) See above. Harvest is best for zombie bear builds cuz your already close to mobs.
4.) I've tried out Life Regen (still have about 1400 on items) and it will not replace LoH/LS altogether but it does helps. You just have to watch out for 'spike' damage. I would recommend looking out for +extra health from globes and potions as an alternative as well.
I do Act 3 Alkaizer runs on MP0 in about 45 minutes which is about 13.5 million exp/lvl with no exp gem or hellfire ring. This is with my ****ty 160% mf gear too. With my other gear I can get to about 29k dps and 1k higher hp.
For weapons, I would just use whats the best items that have dropped. I do suggest using a shield though. With int and crit on it you can still get quite a lot of dps from it.
I LOVE the Grave Injustice passive skill. It synergizes so well with Spirit Walk-Honored Guest(+30% mana), Zombie Bears(you're so close to enemies already) and Soul Harvest(close again). Playing on MP0 helps out a lot since the monsters have so few hp. I think +health from health globes is important too(I've got 8k on my pants) since monsters die so fast you pick up a bunch of globes. The +health globes hp also helps keep your pets alive. My gargantuan rarely dies and all 3 zombie dogs rarely die all at once. Every few minutes a dog dies but I can just resummon and with a 45 second cd and Grave injustice you can summon more really soon.
Even though I have no primary skill I only run out of mana on tough boss packs. Spam Honored Guest for more mana, although you may want to keep it in reserve against Jailor/Vortex packs that spawn fire/poison/arcane/frozen on the ground.
Zombie Bears, even with my crummy 23k dps will kill off packs in 10-15 seconds although if I have to dodge fire/poison/arcane on the ground I slow down considerably. Acid rain is great for large trash packs, killing those suicide things in the keeps depths, killing boss packs at range, dealing with returns damage although with my low dps it usually isn't a problem.
Pretty much what has already said , just wanted to point out some tips / personal appreciationes above them
1) 1h + mojo is better but lot more expensive, specially with the thing of the deep mojo. So my suggestion is just get a cheap skorn from the ah, they are affordable even for the selfound ppl (1m or less easily). Rest of your gear go self find, only skorn would make a big difference for the money and give a great boost to continue finding better gear yourself.
3+4) I can resume this 2 on 1 advice ... I dont have supper gear neither LoH / LS / Life regeneration, and i can keep up well against any combination of elite mob affixes (even reflect) on monster power 4. That leads to the Soul harvest ... As people has pointed out, you can use it as a defensive move with offensive extras (int boost), specially this way: Spirit walk - Healing journey to get ito the enemies (14% max life healing) + Soul harvest - Siphon (10k heal easily when u get used to aim it). The key is to save it / use it as a healing utility, and get used to that playstyle.
Use them with spirit vessel passive to reduce their cooldowns + 3rd auto emergency save healing spirit walk. With this you dont really need any item source of life gaining. Grasp of the dead - Death is life rune is also very helpful and synergyses well with the SW+SH maneuver, and is an all around hability by itself both offensively and defensively.