Solution:

They are sunglasses (sit on the bridge of your nose)

Solution:

One Minute building

building 62 => Sixty second building => One minute building

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

There is no mention if you can use sign or not and thus the only possible way to get this is as follows:

(15 - 9) + (13 - 7) + (7 - 1) + (9 - 1) + (13 - 9)

If you solve inside the brackets, you will get the following equation
6 + 6 + 6 + 8 + 4
Adding all these numbers, you will get 30 which is the required sum.

Solution:

The old lady of course.
After helping the old lady into the car, I give the car keys to my best friend.
And then i go ib the bus with child love <3

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

I spoke with Joe.

Explanation:
There can be only two cases. Either Zoe is a liar or Joe is a liar.

First Case
Let us assume that Zoe is a liar and Joe is a truthful person.
If I asked the question from Joe, the answer will be yes. If I asked the question from Zoe, the answer will be no. Thus in this case, I must have asked from Joe.

Second Case
Let us assume that Zoe is a truthful and Joe is a liar.
If I asked the question from Joe, the answer will be yes. If I asked the question from Zoe, the answer will be no. Thus in this case as well, I must have asked from Joe only.

Solution:

2 people

Say 2 helpers are Helper1 & Helper2

Helper1 food Helper2 food McDuck's Food
End of Day 1 : 1 4 4
Now 'A' will head back

End of Day 2 : N/A 2 4
Now 'B' will head back

Now Mr. McDuck have 4 day food :-)

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

Remove the same 2 matchsticks from each figure and move figure towards left 45 degrees, It forms the letters V W X Y.