I would recommend reading through Tips and Notes - all the important explanations of the lessons are given.
IPA Notes Examples A [ɑ] as in "palm tree"; never as in "hat" Ä [æ] like the letter a in "band"
The dots above Ä and Ö are NOT accents nor stress marks used to modify A and O. The two letters stand for distinct sounds made in the front part of the mouth, whereas the sounds represented by the dotless letters are produced at the back. Forgetting your dots results either in incomprehensible gobbledygook or in some wholly unrelated word. It is better to tell someone that they are hellä (tender, gentle) than to call them hella (kitchen stove).
In German, those two dots over a letter are called an umlaut. If they have a keyboard that does not have an umlaut, they use "ae" or "oe", because that is how "a" with an umlaut and "o" with an umlaut are pronounced.
Finnish has a lot of umlauts. In other courses, there are rows of letters with accents. Click on one, and you get a letter with an accent over it. I hope Finnish will add that feature.
The French also use umlauts, but theirs show that the vowel with the umlaut is pronounced separately from the letter after it.
The “umlaut” in French is actually called a diaeresis (or tréma in French) because it doesn’t change the sound of the letter (like in German), but shows that a vowel with the diaeresis is pronounced distinctly from the previous letter, as you said. Because they have different uses, the umlaut and diaeresis are considered different diacritics.