Some ritual spell cards, like as "Advanced Ritual Art," can mitigate this by utilizing monsters from the main deck rather than monsters from your hand or side of the field. These cards are called "mana burners" because they consume mana in order to cast their spells.
Other ritual spell cards, like "Rite of Flame" and "Ritual Summon", summon monsters from your hand or field. These cards aren't called "mana burners" since they don't require any mana to cast.
Finally, some ritual spell cards have multiple effects. For example, you can activate an effect when you play a ritual spell, then activate another effect when one of those rituals is destroyed by battle or card effect. These types of cards are called "combo pieces" because they can be used together to create a large number of possibilities. An example of such a card is "Twilight Constellation". When you play this card, you get to choose either to destroy a monster on the field or draw two cards. If you choose to destroy a monster, great! That's what we wanted to happen. If you choose to draw cards, that's also fine. The card doesn't care which choice you make as long as at least one of them happens.
Ritual Monster Cards are put in the main deck and cannot be summoned until all of the necessary cards are in your hand or on the field. When they do appear, you must shuffle them into your hand before searching for more cards to add to your hand.
So yes, Ritual Spell Cards remain on the field when they're activated and can't be removed unless one of the conditions for destroying a card is met (destroyed by an opponent's card effect, for example).
Furthermore, if you activate a Ritual Spell Card and ignore its activation cost, then it will remain on the field forever. Even if you remove all of the cards from the field, the Ritual Spell Card will still be active. To disable a Ritual Spell Card so that you can't use it again, you need only pay its activation cost, even if you forget about it later.
For example, say you have a Ritual Spell Card on the field called "Dread Wand". You need to pay 1 credit to activate it. If you can't pay 1 credit now, but you remember later that day that you have some money coming in tomorrow, then you can pay at that time.
Ritual Monsters are unique monsters that can only be summoned with a ritual spell card and a specified tribute. At the end of each turn, you draw a new Ritual Monster Card from your deck over yourself.
Yes, you can use the ritual spell card to summon your own Ritual Monsters if you have them in your hand or on the field. You can also pay tributes to make other players lose their monsters if you want to force a battle between two specific players. Finally, if you control any monster that was banished during the previous turn's end phase, you can bring it back using its effect when you perform a ritual spell.
Note that since Ritual Monsters are drawn into play at the start of your turn, they will never escape the battlefield. This means that if you target one with a spell or attack, it will never come back into the game. Be careful not to waste your resources by summoning monsters that you'll never use.
The exact rules for rituals are found in Rule #5. They're quite complicated so we'll just go over the basics here.
First, there is a ritual spell card that can only be used to summon Ritual Monsters.