If i have a removal spell and my opponent sacrifices a creature to, let's say Altar of Dementia. Can I prevent the sacrificing by casting my removal spell to the creature being sacrificed? Or not?
The sacrifice of the creature for Altar of Dementia is part of the cost of the ability on Altar of Dementia. As it appears before the : on the ability, all actived abilities are templated [COST]: [EFFECT]
Now for the important bit, paying costs of an spell/ability can't be responded too. So by the time you would receive priority in order to cast your removal spell, the creature has already been sacrificed.
In general, while your opponent casts a spell or activates an ability, no player has priority, so no other player can cast spells or activate abilities (including those that would keep your opponent from paying the spell or ability's costs) (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated; C.R. 117.1a-b).
EDIT (Aug. 11, 2018): Add rule citation.
EDIT (May 15, 2019): Edited rule citations.
EDIT (May 14, 2021): Some rules were renumbered in the meantime.
If i have a removal spell and my opponent sacrifices a creature to, let's say Altar of Dementia. Can I prevent the sacrificing by casting my removal spell to the creature being sacrificed? Or not?
No.
In general, you can never respond to actions, only to spells and abilities. When a player casts a spell or activates an ability, that casting (or activating) is one uninteruptible block of actions: the player announces the spell/ability, puts it on the stack, makes any and all necessary choices (like modes, targets, alternative and/or additional costs), then calculates and pays the costs. Only once this block of actions is completed do players get the chance to do something again. Now the spell/ability is on the stack, and now you can respond to it. But since the costs have already been paid, you cannot retro-actively prevent your opponent from paying them.
So if the sacrificing is part of the costs (as it is for Altar of Dementia), you cannot stop your opponent from sacrificing something to pay those costs.
As a reminder, activated abilities have the form "[cost] : [effect]" (note that this form can be hidden in the CompRules for some keyword abilites, e.g. Equip). Note the colon: everything before the colon is the cost of the ability, and any actions called for in the cost part happen before you get a chance to react.
Last question, my opponent casts Omnath, Locus of Rage. Now the creature is in play and i've decided to Play a removal spell. Can he respond by playing a land? So that he will still get an elemental. Or he isn't allowed to play land in response. If he is allowed when can i cast my removal spell so that he will not be able to respond on playing a land.
Yngre u can only play a land when you could play a sorcery. It is hard to responce with a land when something is on the stack as only ikstant speed things can be used (instants and activatef abilaties).
How ever, if your oponent played the creature he has prioraty after it resolves. If he plays a land (lands do not use the stack as you play them) you can only respond to it after the triggered abilaty is on the stack. (A triggered a abilaty starts with when, at the beginning etc)
While this does not solve yourproblemlook into the split second cards from timespiral block.
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Now for the important bit, paying costs of an spell/ability can't be responded too. So by the time you would receive priority in order to cast your removal spell, the creature has already been sacrificed.
EDIT (Aug. 11, 2018): Add rule citation.
EDIT (May 15, 2019): Edited rule citations.
EDIT (May 14, 2021): Some rules were renumbered in the meantime.
No.
In general, you can never respond to actions, only to spells and abilities. When a player casts a spell or activates an ability, that casting (or activating) is one uninteruptible block of actions: the player announces the spell/ability, puts it on the stack, makes any and all necessary choices (like modes, targets, alternative and/or additional costs), then calculates and pays the costs. Only once this block of actions is completed do players get the chance to do something again. Now the spell/ability is on the stack, and now you can respond to it. But since the costs have already been paid, you cannot retro-actively prevent your opponent from paying them.
So if the sacrificing is part of the costs (as it is for Altar of Dementia), you cannot stop your opponent from sacrificing something to pay those costs.
As a reminder, activated abilities have the form "[cost] : [effect]" (note that this form can be hidden in the CompRules for some keyword abilites, e.g. Equip). Note the colon: everything before the colon is the cost of the ability, and any actions called for in the cost part happen before you get a chance to react.
Last question, my opponent casts Omnath, Locus of Rage. Now the creature is in play and i've decided to Play a removal spell. Can he respond by playing a land? So that he will still get an elemental. Or he isn't allowed to play land in response. If he is allowed when can i cast my removal spell so that he will not be able to respond on playing a land.
How ever, if your oponent played the creature he has prioraty after it resolves. If he plays a land (lands do not use the stack as you play them) you can only respond to it after the triggered abilaty is on the stack. (A triggered a abilaty starts with when, at the beginning etc)
While this does not solve yourproblemlook into the split second cards from timespiral block.