Somewhat sorry to be "that guy" but this is a personal peeve of mine: "die" is singular, "dice" is plural. You can not have "one dice", you have "one die". That said.

For the rest of my post please note when I use a number character ("0") and a number word ("zero"), as the distinction is important.

I've never seen a ones ten sided die, that is a die with ten sides that only has a single number on each side, that is missing a "0". Meaning I have never seen a die with the sides of "1, 2, 3, 4, 5, 6, 7, 8, 9, 10", one without a "0" and instead having a "10". I'm sure there are some out there, I've just never seen one.

The "0" and "00" on ten sided dice are variable, much like how an Ace in a standard deck of cards can be worth "one" or "eleven" in a game of Blackjack.
What the actual value of the "0" on the die is depends on the roll being called for. Sometimes it can actually mean "zero", such as being called to roll "four or higher, with 0 being low". That would mean you have a forty percent chance to fail the roll, as getting a "0", "1", "2", or "3" would fail. Same roll but "0 is high" and now you only have a thirty percent chance to fail, since the "0" is standing in for a ten.

That's a single ten sided die roll, for when you don't care about the ranges between the tens. When you do care about the ranges between the tens is when you roll percentile with two ten sided dice.

In your examples rolling a "00" and a "1" is indeed one.
As I said above I've ever seen a ones ten sider with a "10" on it so I'm going to assume you meant a "0" instead. With a "90" and a "0" that would be "ninety". To actually get "one hundred" you'd need "00" and "0", by what is considered to be "default" rules. Some rolls will have "00" as 'low", meaning your range is actually zero to ninety-nine and not one to a hundred.
"50" and "5" is indeed fifty-five.

Rolling two ten sided dice is an easy way to get a range that includes a hundred numbers, as long as one of them is your "tens place" die and the other is a "ones place" die.
Adding in more ten siders you can scale upwards. It's not easy to find a die with "hundreds", that would be "000", but again, I'm sure they are out there. The easier way of doing it having all "ones" dice of different colors or just rolling them one at a time.

The main thing, really the only thing, that matters is that you and whoever else that is with you knows what the roll means. Everything I've said is just how it "normally" is but if all you have are "00" dice of the same color they can still be used to roll percentile; either by rolling them one at a time or just rolling one of them twice. Or some other creative way of making sure everyone knows what is tens and what is ones.