You asked interesting questions. They indicate that you seek a deeper knowlege of your sport. You are standing on the line that separates a sport from an art. You ask questions that might take some many years to even think to ask, let alone discover an answer. Let me address them as you asked them:
1. Are these types of counters real ones, or are my sources wrong in any way? (Stop-counter and Cross-counter)
The Stop-counter or Stop-hit is real. Although it does not actually start before an opponent attacks. It only appears that way. Using a Stop-hit requires the boxer to "read" when and how an opponent will attack and then strike an openning before or just as the attacking movement starts. An attack actually starts with preparatory physical positioning and physiological signs of mental preparation for an upcoming explosive action. These actions are actually the "start" of an attack. So you see, a Stop-hit only appears to start before the attack. It only starts before the mechanical part of an attack begins.
Here is something to ponder: Can you cause an opponent to attack at the time you wish, to the target you wish, and with the weapon you wish? If so, how?
The Cross-counter is a true counter. A counter is a reaction to an attack with a preventative move and then an attack that takes advantage of the final position of the opponent after his or her attack is complete or during the attack. You mentioned striking over the top of the opponents extended arm.
Consider this: Can you counter strike the the body? If so, how?
...................Can you attack the head in a striaght line from a different
...................angle? If so, how?
...................Can you counter-attack the head using a circular or corkscrew
...................If so, how?
2. Are there any other methods of countering? If so, how are they performed?
The answer is yes; There are three that come to mind immediately:
Are you aware that you can prevent an opponent from even thinking to attack a certain way by (a) your body position and (b) your actons? (c) There is a technique called a Bridge-punch that martial artists use which can be applied to boxing.
(a) Most boxers know about bobbing and weaving. Most boxers know about popping jabs to keep an opponent off-balance. That is not what I am talking about. I'm talking about positioning your arms, hands, feet, and body to make your opponent uncomfortable to throw a certain technique.
For example: If you know your opponent has a strong right hook, you might want to make it hard for him to use it. Two tactics would make it uncomfortable for an opponent to throw that right hook. First, when you attack you should step slightly further to the opponent's left then normal and your right foot should finish outside and slightly behind the opponent's left foot. Continue your recovery from your attack by sliding away to his left with your right foot and into your stance. Second, when your opponent attacks, slide toward him to his left as you slip and counter or away in a circling motion to his left. It is difficult to throw a right hook when your opponent is always moving to your left.
When you want him to throw the hook, simply move normally and wait for your opportumity to counter it. He will eat up the opportunity because he has been frustrated up to now.
(b) Boxers are taught to look for certain positional ques to decide what punches to throw.
For example, if an opponent always drops his or her right as he or she throws a left jab, you might counter by slipping and throwing your own left (jab or hook) to the head. Knowing this, you can drop your right a time or two as you throw a jab and then keep doing it until your opponent tries the counter. When it comes you can slip and counter-hit.
(c) The Bridge-punch crosses under and inside of the opponent's punch to your head, deflecting it. You catch the opponent's punch with your forearm just below your elbow as you extend your arm to punch to his chin. When you turn your punch over do it earlier and continue turning it 90 degress more than usual. This adds your opponents downward force to your punch, giving you more power. As you execute this technique you should move forward diagonally to your opponents right. Remember to keep your chin tucked unless your like getting punched in the chin.
Let's continue this dialog---