Cavalary: I *think* you need to be a mage to get mana at shrines. But not sure.
Edit: Checked
a list, not quite. Seems like as a novice you ONLY get mana, while as a mercenary you NEVER get mana.
And str from apples and mana from mushrooms seems to still work.
OldFatGuy: I'm still guildless, so all should be available. After you become militia or mercenary, mana isn't available. After you become a mage, strength and dexterity aren't available. But guildless, they're all supposed to be available.
Found this FAQ on how shrines work:
vsr: The Hero can pray to Innos 1 time per day. During a prayer you should to spend 100 gold coins, otherwise the bonus won't be. Thus the Hero receives randomly +1 to strength/dexterity/mana.
The quantity of bonuses doesn't depend from chapter, but only from guild to which our Hero belongs:
Neutral/Militia/Paladin: 10 times to strength, 10 times to dexterity, 20 times to mana, then +3 to life indefinitely;
Novice/Fire magician: 20 times to mana, then +3 to life indefinitely;
Mercenary/Dragon hunter: 10 times to strength and 10 times to dexterity, then +3 to life indefinitely.
If not to spend money at all, then with probability of 5% Hero will receive +1 to life;
If to spend 10 coins, then receive +1 to life;
If to spend 50 coins, then receive +2 to life.
Source.
I've tested it as a guildless and it's true - you get randomly strength OR dexterity (10 each overall), only then you start getting +1 mana (20 mana overall), then +3hp (unlimited).
Exactly in this order: strength and dexterity, then mana, then hp.