Yes
"A penny" isn't an idiom - it's just a one-cent American coin.
The words cent and penny are synonymous; a cent is a penny.
No such coin. A penny is one cent so a 2 cent penny does not exist. There are US Two- Cent pieces but a date is needed.
a penny means that it is a kind of coin that is worth 1 cent.
That would be cent, as in 1 cent is the same as 1 penny.
A penny stock is one that is relatively cheap and does not actually mean that the stock is one cent. The penny stocks are usually high risk but high reward.
i cent
One cent.
penny
It's worth exactly one cent.
There is no difference between penny stocks and cent stocks.
Assuming you mean a U.S. cent and not a U.K. penny, yes - it's worth its face value, but nothing more.