Yes.
Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.
If the signs of both numbers are the same, the product will be positive. If the signs of the numbers are different, the product will be negative.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
The product is obtained by multiplying two numbers. The product obtained by multiplying a number by 1 is equal to the number, i.e. 1 x 10 = 10(product). Therefore the product of any number and 0 is always 0.
This is not a general valid rule; ions have a different number of electrons.
It is equal to 1, but not always: the reciprocal must be defined for the equality and the reciprocal is not always defined.
In an atom, the number of protons is always similar to its atomic number. (The number of nutrons may be similar or different.)
In a neutral atom, the number of protons is always equal to the number of electrons.
No. The sum of two negative numbers will always be a negative number. If, however, you multiply the numbers, their product will be positive.
No. If the rational number is not zero, then such a product is irrational.
Yes, the amount of protons within the atom is always equal to its atomic number. If a proton is removed, you get a different element.
Yes a number multiplied by zero will always equal zero if you talk about integers. If you talk about limits, it's different.