Spirit Visage's passive is a unique multiplicative increase, so if you had 10% life steal before, you will now have 13%, and not 40% life steal (10% × 1.3 = 13% life steal).
Spirit Visage's grants a total of 160% base health regeneration because its passive increases the effectiveness of a champion's base health regeneration (+30%) and its own 100% (+30%).
I'm most concerned about Udyrs' Turtle healing, runes including conqueror, bloodline, taste of blood, ravenous hunter and items such as Ravenous Hydra, Titanic Hydra, Cinderhulk and Bloodthirster.
Spirit Visage multiplies all healing by 1.3. So lifesteal values are effectively multiplied by 1.3 (10% -> 13%), base HP regen multiplied by 1.3 on top of being doubled by the other passive (2*1.3=2.6). Multiplied by 2.6 means increased by 160%.
It's the exact same thing for other sources of healing, so all the healing runes/items you mentioned like Turtle stance, conqueror, ravenous hydra etc also have their healing multiplied by 1.3.
Technical question: Alistar heals himself with his E, which says that nearby allied units will be healed for half the amount. If this half the base amount of half the amount including the Spirit Visage passive bonus?
Spirit visage:
"UNIQUE Passive: Increases your healing, regeneration and drain effects on yourself by 20%"
Perseverance / Garen Passive:
"If Garen has not taken damage from any source except minions in the last 9 seconds or affected by an enemy champion's abilities, he will start regenerating 0.4% of his maximum health per second."
Spirit Visage's passive is a unique multiplicative increase, so if you had 10% life steal before, you will now have 13%, and not 40% life steal (10% × 1.3 = 13% life steal).
Spirit Visage's grants a total of 160% base health regeneration because its passive increases the effectiveness of a champion's base health regeneration (+30%) and its own 100% (+30%).
It's the exact same thing for other sources of healing, so all the healing runes/items you mentioned like Turtle stance, conqueror, ravenous hydra etc also have their healing multiplied by 1.3.
It's really simple :)
Does this mean starcall would heal more when soraka wears this or just meh?
Yep, it would increase
Does the passive work with Mundo's passive?
Yes, along with his ult and the amount of healing from landing Qs.
Spirit visage:
"UNIQUE Passive: Increases your healing, regeneration and drain effects on yourself by 20%"
Perseverance / Garen Passive:
"If Garen has not taken damage from any source except minions in the last 9 seconds or affected by an enemy champion's abilities, he will start regenerating 0.4% of his maximum health per second."
So yes, it does work together.