Yes. I don't know how many skill points are available in the game, and you may sacrifice some other skills (ie. combat related), but you can level every crafting in game on one character.

yes
Skillpoints will be a bit tight after collecting Skyshards and before making PVP and Cadwels silver and Gold. But finally you will have enough for all you want.
http://tamrielfoundry.com/skill-points/

Yes but you may want to start researching right now Researching traits takes time, a lot of it.

There're plenty of skillpoints, my main has all crafts, all class skills/passives, light armor, heavy armor, destro, resto, mages' guild passives, a few fighters' guild passives, some mages' guild active skills, all alliance war passives, some Legedermain/TG things, UD etc and still has a few skillpoints left. Admittedly that's almost every skillpoint in game aside from ~25 PvP ones and DB questline.

Hello
I wish you good luck with crafting - it's very enjoyable.
An option not mentioned is to use a new character just for crafting. I started on NA with a Crafting Alt when bag space was a problem and ran around all zones collecting skyshards - you need 90+ points to max out all crafting skills. I actually had 3 crafting alts at the time (pre ESO+) for storage and crafting. Been on EU for 3 months with one Crafting Alt and doing Master writs now. It's very easy to do and you can just spend all your skill points in crafting.
There's only one slight problem with access to the Earth Forge and Eyevea but you just have to complete the Mages and Fighters Guilds quest lines on the alt.
Whatever you do I suggest starting research ASAP - it does take ages.
Once Certified as a Crafter do all 6 writs daily and if you can find Intricate or high level items for deconstruction it will boost your skill. Enchanting is the slowest to get to level 50.
Good luck.

Yeah better with one character too so you don't log in and out to do crafting. Just be patient and farm skyshards with that one character.

Yes.
There are many ways to go about crafting. I have friends who have everything on one character, and friends who have each profession on a different character.

Personally, I have on "Equipment Crafter" and one "Consumables Crafter" and it worked out well until furniture came out. :-P

Yes it is. I have and so have many others. You just need to do all the main quests for each DLC, faction and main story also get as many skyshards as possible.


Blacksmith
Tailoring
Woodcraft

These are extremely easy to lvl up. Focus on researching every possible trait. If an equipment has no trait or if you already know the trait, deconstruct it. That yields quite a lot of exp. Perhaps even more than crafting to lvl up. Also do the daily writs they yield nice exp rewards.


Enchanting

Same as with the ones mentioned above. Break apart any glyph you have. glyph traded from other players yield more exp if you break em. A bit tedious but not impossible, for me this was the hardest one to max out.


Provisioning
Alchemy

These are a bit tricky at first. You cant break these apart so you'll need to craft often. As you play around the world gather as much ingredients and recipes as possible and craft in bulks to make the best of time. Writs are helpful here too. If you have the gold to spare buy the ingredients and recipes from players it will save you a lot of time