For example, in the game Link eats a dish which gives heat-resistance boost for a given length of time and eats a dish which increases attack power for another given length of time, will Link have both ability boosts to keep or will the ability boost from the newest dish overwrite the older dish?
No, you cannot combine buffs by eating multiple foods/elixirs. You can, however, combine a food/elixir buff with armor buffs. If you eat a second food/elixir, the newer buff will overwrite the older buff.
How to get a buff
Link can gain a buff (positive effect) by wearing certain pieces of armor or by consuming certain foods/elixirs. Whereas armor buffs apply whenever the armor is worn, food/elixir buffs have a countdown timer (length varies by ingredients).
(Note: In this post, the term "armor" includes all clothing and items which can be equipped to Link's head, torso, and legs.)
When buffs are unstackable
No single food/elixir may provide more than one buff. Further, when a food/elixir buff timer begins, it overwrites any existing buff timer Link was enjoying. Thus, food/elixir buffs aren't stackable with other food/elixir buffs (but they can be combined with armor buffs; see below).
Combining different buffs
Multiple buffs may be combined by mix-and-matching armor pieces (for example, wearing a piece of Attack Up armor with a piece of Stealth Up armor), or by using a food/elixir buff with one or more armor buffs.