You can place as many on the field as you wish. That is to say, if you somehow had 10 Spell Cards in hand, you are allowed to activate them all - you'd activate one, let it resolve, and it would go to the graveyard after.
Keep in mind though you have only 5 regular S/T slots, and a Field Spell Card slot. If you activate any continuous Spells, or Set a spell, then these are taking a slot up. If you fill all your slots like this, you cannot activate any other cards until a slot is freed up.
You can't ever just discard cards for no reason, you can only do so if instructed to by a card effect or a game rule, such as the one that lets you replace one Field Spell Card with another.
there is no limit
No, there isn't. Unless you count a Field Spell Card, which is a spell card but has its own zone, so technically you can have 6 spells active.
Depends on the field spell. Inherently, Armityle has no effect that says he is immune to the effect of field spell cards.
You may replace your active Field Spell card with a new one, either Setting it or Activating it. Your old card is destroyed and goes to the graveyard. Replacing an active Geartown by Setting a second one is a focal combo in Geartown decks. If your opponent has a Field Spell card active, this is destroyed when you resolve a Field Spell card. However their active one is not destroyed if you just Set one, and neither is their Set one destroyed if you activate or Set one too.