I'm new to this game. I was wondering if I can make an Armor Spell become permanent with the Initiation ability called Vivification. If I can, how much karma is needed for that?
Vivification is not the official name of the ability you are talking about, it's Quickening. I'm aware that some languages (like Portuguese) translated that to Vivificar, which is a similar concept but with a larger background. Anyway, here is how the mechanic works:
Instead of sustaining the spell, and taking a -2 (or -1 with the right quality) penalty on all checks, you may decide to Quicken the spell, spending n points of karma, 1 per point of Force you want to use on the spell (a minimum of 1 point of karma, maximum of the Force used), then cast it normally to decide the effects if necessary (note down the net hits). Then you no longer need to sustain the spell, the metamagic ability is doing that using the karma you spent on it. Additionally, if anyone tries to counterspell and remove the spell from the target, you get an additional pool of dice equal to the karma spent on it.
Example, you want to cast levitate with force 4, you spend up to 4 karma, cast levitate and now you no longer have to sustain it. Anyone trying to remove the spell will have to pass on a check using their Counterspell+Magic[Astral] versus your spell's Power (4) + Magic + 4 (the karma spent), so 8 + your Magic attribute, since you used a force 4 spell.
The Initiate Power you're refering to is called Quickening, not Vivification, see p. 326 core rule book.
When you quicken a spell you need to choose a number of karma points between 1 and the force of the spell. Within this range it's your choice how much karma you want to spend. The only benefit of spending more Karma is a higher pool against dispelling.
Quickening: [...] To quicken a spell, take a Complex Action and spend karma while you're sustaining the spell. You must spend at least 1 Karma but may spend up to the Force of the spell. The spell becomes permanent and gets a dice pool bonus against dispelling (p. 295) equal to the amount of Karma you spent on it.
You indeed can make an Armor spell "permanent", but be aware that the karma is gone, if you drop the spell or if it gets dispelled. Furthermore as a runner you may encounter security mages/spirits that may notice the active spell which could get you in trouble...