I'll answer the easy question first.
Position size calculations are done exactly the same way for long or short positions. This is true for calculations done by hand, and for calculations done by the Position Size Calculator.
If you open up the Position Size Calculator and work with it, in order to understand what it's doing, you will notice that it never asks you whether you are trading long or short.
Obviously, you are currently studying how to do position size calculations manually (without the Calculator). And that's a good thing. When you're a beginner, it's important to know how and why things are calculated the way they are, before you take the shortcut of letting the Calculator do the work for you.
So, now let's tackle the thorny part of your question.
Despite what the School lessons are teaching, there is no buying or selling of currencies, or currency pairs, in the retail forex business (our tiny corner of the huge, worldwide foreign exchange market).
Your broker doesn't maintain an inventory of foreign currencies to sell to you, and he isn't in the business of buying currencies from you.
Instead, he is in the business of taking the other side of your trade, whether long or short, at a price which he dictates. This places him in the position of counterparty to your trade, and he remains in this position until your trade is closed.
So, if your long trade does not involve buying the base currency and selling the quote currency, and if your short trade does not involve selling the base currency and buying the quote currency -- as the School lessons incorrectly teach -- then what exactly is happening when you place a trade?
Your trade is simply a bet on the direction that a particular price will move. And your broker simply holds the other side of your bet.
If you take a long position in EUR/JPY, for example, you are simply betting that the price of euro, as quoted in yen, will increase. And you are able to place this bet with your broker at any time during the 5-day trading week, because your broker has determined that he will accept your bet at a price agreeable to him. That price is called the ASK price (it's the price your broker is asking, in return for the long position which you wish to take).
And, similarly, you can take a short position in that pair, or in any other pair, if you agree to do business at the BID price dictated to you by your broker.
So, at any given time, your broker is offering to take either side of any bet which you choose to place.
Confusion enters the discussion when these long or short positions are referred to as buying or selling. Those terms are perfectly valid in many other markets. But, they simply are not valid in our retail forex market. However, the terms buy and sell have been carelessly used by forex traders, forex brokers, forex teachers, and our own beloved School for so long, that we will never get rid of those terms. And, quite honestly, they are a convenient short-hand. It's a lot easier to say "buy such-and-such", than to say "take a long position in such-and-such".
Consequently, we have misleading terminology, which we all persist in using, even though we know that it's misleading. -- As if this stuff wasn't complicated enough, without being tripped up by misleading terminology!
So, when you take that long position in EUR/JPY -- which everyone carelessly refers to as buying EUR/JPY -- your account currency (whatever it might be) will never be converted into either EUR or JPY. You won't buy or sell any foreign currency. And, for the entire duration of your trade, you won't own anything except the balance in your account.
Let's say your account is denominated in USD -- that's the currency you deposited into your account. In this example, USD is the currency in which all your account metrics (balance, equity, P/L, pip-values, etc.) will be reported to you. As we'll see in the following example, pip-values in currencies other than USD must be converted (mathematically) into dollar-values.
Let's stick with the example of a EUR/JPY trade in your USD-denominated account, and walk through the position-size calculation.
Let's say you want to take a position in EUR/JPY (it doesn't matter whether this is a long or short position), you want to limit your risk on this trade to $10, and you want to set your stop-loss 50 pips away from your entry price. The only thing you don't know yet is how large a position to enter. That's what the position-size calculation is all about.
Your stop-loss limits your possible loss on this trade to 50 pips, and you want this loss (in pips) to correspond to a dollar-loss of $10.
First, we have to determine what a pip is.
In this trade, JPY is the quote currency. (In fact, in any yen-pair, JPY is always the quote currency, never the base currency). Therefore, in this trade, a pip is 1/100 of one yen per unit of currency traded. And 50 pips is 50/100 of one yen, or ¥0.50 per unit of currency traded.
For a trader with a USD-denominated account, that's not very usable information. So, we need to convert ¥0.50 to its equivalent in USD. For that, we go to the current USD/JPY exchange rate -- let's say it's USD/JPY = 110.80 -- and we calculate that ¥0.50 = $0.0045126. In other words, one-half of one yen is a little less than one-half of one cent.
Now we can say that a 50-pip loss in EUR/JPY will cost $0.0045126 per unit of EUR/JPY traded. And we want to know how many units of EUR/JPY to trade, such that a 50-pip loss will cost $10.
We get the answer in one final calculation:
number of units of EUR/JPY = $10 / $0.0045126 = 2,216 units
If your account does not provide for trading in individual-unit-amounts, then you will have to approximate 2,216 units as, for example, 2 micro-lots.
We can confirm that the result calculated above is correct, by entering the appropriate metrics into the Position Size Calculator. After the result is calculated, it looks like this:
Notice that it was necessary to assume an account balance, and a risk percentage, corresponding to the desired $10 risk amount in our example above. Any combination of account balance and risk percentage corresponding to that $10 risk amount would produce the same result in the calculation. Play around with the Position Size Calculator, and prove this to yourself.
Notice also that -- as said above -- it doesn't matter whether the trade being contemplated is long or short. 50 pips in the "wrong" direction (against your position) is all we're concerned with, when equating loss to risk.
I'm aware that I have shown you a different way to do the position-size calculation, from the way presented in the School lesson. I hope that a different perspective will help to clear up your confusion.