According to Zenimax, you should be able to fully flesh out 2 proffs per character and not gimp your pve/PvP. I'll be trying all though cause I'm not too bothered about end game as I live to craft.

They say you'll finish with about 200 skill points.

The bare minimum you'll need in crafting is:
Alchemy - 7
Blacksmithing - 9
Clothing - 9
Enchanting - 13
Provisioning - 9
Woodworking - 9
Total - 56 skill points.
You'll be able to create full power everything with this investment - only not as much or that easily as a dedicated crafter. But 56 is a full crafter build, everything else is convenience.

You'll have then 144 skill points to flesh out your toon. That's enough for about two full builds without any overlapping (so 4 different weapons, totally different armors, absolutely different passives - let's say this is highly unlikely). I'd say you can be a full-time perfect crafter and a 100% PvE-PvP toon at once.

And also note that there are about 300 skill points in the game. That is more than enough even for convenience.

I agree with your points, Zamiel. I chose, however, to go with crafting alts not so much because of skill point concerns as inventory concerns. There's just so many materials to collect. I realize it's possible to use up the materials of a given tier of crafting and move onwards to the next to save on inventory space, but I find just dumping the stuff in the bank and withdrawing it on crafting alts much easier.

This system of mine will allow me to feel free to dump points into all the crafting skills without worrying about gimped characters. I've gone with three crafting alts:

Blacksmith/Clothier/Woodworker (make efficient use of racial motifs!)
Alchemist/Enchanter
Provisioner (lots of mats to collect for this one profession)

Meanwhile my main character is a non-crafter giving me freedom to dump points into anything. The crafting alts will allow me to test out stuff on the other three classes that might interest me. I'm confident I can put together viable PvE builds with them early on in order to start gathering points for the crafting lines. If I understand late-game correctly, points start coming fast and furious so I expect I won't have to take any of these crafting alts beyond my home faction's land into veteran ranks territory before I have three fully-fleshed out crafters.

Is it possible to have an alt level 1 to be crafter? Or you need levels to be able to craft?

Crafting uses the same skill points as everything else... so while you can level up your crafting with a level one alt... you will need skill points to put them into the ability to be better at crafting. You ultimately have to adventure to get skill points to have your crafter be able to advance and get better... just like your fighting ability.

The main point I would say is that there is no actual level requirement... just skill points... so if you focus on crafting with your skill points you can get very good at it with lots of perks quickly at low level... but your combat will suffer if you try and go too fast into crafting.

It currently takes 137 skill points to max every perk in each crafting profession... so with over 300 skill points in the game you COULD master them all and still have more then enough points to make an effective combat character. It will take a long time and really take some creative use of storage space for mats as you do it. But it is very much in the realm of possible and effective if that is your goal.

I know as I do not PvP that frees up a lot of skill points for crafting.

Level an alt to level ~level 10, get all the skillpoints needed for a single crafting proffesion. Send everything he can deconstruct from your main to your alt and you can have a pure crafting character with very little actual fighting time needed.
although level 8 can probably also be done