There isn't any difference between "to wrap" and "to wrap up". The "up" can't even be really logically explained, which is perhaps why some people have not posted an answer. There is no concrete explanation or rule for when to add "up".
It's actually kind of nonsensical, because you're not applying the wrap in an upward direction, motion, or anything of the sort. It actually adds no additional information to the statement and does not change the meaning of anything. It's simply superfluous, unnecessary, and its addition is just a matter of personal preference.
The only additional implied meaning it can have in some situations is the implication of completeness. "Little Jimmy was all wrapped up in his blankets." By adding "up" here, it is loosely implied that Jimmy was entirely wrapped up in his blankets, covering him entirely. However, this does not concretely mean that if "up" was used here, then Jimmy must have been completely covered in his blankets.
Like I said, it's more a matter of personal preference to add "up" here, it doesn't hold any concrete meaning and is most likely technically incorrect, but widely used and acceptable to use.
To address the examples you provided. They are all technically correct/acceptable speech, but
Please wrap the tinfoil around the food.
would be perceived as very robotic. The reason why is because you're being very explicit with this sentence, instructing someone not just to wrap the food, but how to wrap the food with "around the food." It's very strict, explicit instruction that doesn't really need to be so explicit unless you are teaching someone how to wrap up food.
There is very little difference; one of them has a more formal register than the other.
In Britain, we normally use the preposition phrase "out of", and that's accepted in formal English. In informal use, some dialects regularly omit the "of", and it is understood in context. I don't recommend this form when you are writing.
Other regions appear to have this distinction reversed.
As an alternative, you could also consider, "He gazed through the window", but that is slightly different, as that can mean gazing in to rather than out of.
Best Answer
There is very subtle difference between decide sth and decide on sth.
Decide on is used to choose something from a number of almost similar possibilities(ppssibilities that would yield almost similar results, but it depends on your personal choice )
e.g
This sentence implies that we have different venues that we can choose from.
It implies we have different colours available like red, green etc.
When you say
This means you have different shares that you can give for example you can give them 5% share,2% share and 9% share.
If you say
It does not necessarily mean you have different equal possibilities (possiblities having similar results)