Some Food Skills give the same effect as Armor Skills, such as Felyne Woodsman and Whim. If I get both of these skills, do their effects stack or does one override the other? If it is the second case, does the one that provides the most benefit stay or does Armor Skill always trump Food Skill (or vice-versa)?
Kitchen skills give two types of boosts: "Food" skills, and Felyne skills. The food skills give health (based on the combined stars, up to 50 max), stamina (50 max as well, based on Freshness), and one other skill (Attack, Defense, Resistance, Tipsy, etc.)
These Food skills will always stack. Without the Felyne Foodie skill, you will also lose them upon death.
The tricky ones are the Felyne Skills. Some are unique, in that they provide a skill that can't be gotten any other way, such as Explorer, or Carver. These don't stack, because there's nothing to stack with. Others are binary buffs, in that they either work or don't, such as Heat Res (Armor Skill), and Firewalker. Both allow you to walk on lava edges with no damage. Getting both does nothing, because there's nothing to improve.
For the rest, they will stack, up to the limits of whatever is being increased; both Gathering and Felyne Gathering up the chances of hitting maximum node gathers, but they can't do anything beyond that. Same with Speed Sharpening and Polisher; one swipe is the minimum, so Polisher adds nothing.
Those that add to numerical values will be tested as I can, but current observations show that as long as the internal limit isn't hit, they do stack. As to what those maximum values are, that differs depending on the skill. There has to be a non-0% chance of things happening (such as Whim and Woodsman combining), or gathering would be trivial, as nothing would break, and you'd never need to replenish your pickaxes or bug nets.
I have tested these, and will add as I test more:
No it does not combine it's effects but just overwrite the weakest effect to a the strongest one. A simple example would be testing fast sharpener on food which will shorten your sharpening time by 2 shaves and sharpener which reduces it to 1 shave, both reduces the sharpening time and the highest one overwrites it's predecessor skill.
There are some stack-able bonuses though, if you are looking for something of the sort. You may stack a power seed, power pill, max attack damage, the two shakalaka's high level power up, mega demon juice, sleep,heroics(when hp is at 10% you get a 75% damage boost and also note that this is an individual unique skill) and a first critical skill on a great sword. One hit a kut-ku :D.