Hey, is the purpose with the beginner lessons to follow each day separately? Then build up the more advanced I get?

I also feel strain in my throat when I do the warmup lessons. Should I maybe watch another video before I follow the course to learn how to relax more or do you have any other tips? Or just keep going? Im at day 3 now.

Yes! Please read this article for more guidance: https://www.30daysinger.com/blog/one-lesson-per-day-how-to-practice-for-the-best-results

As for straining: you can always drop out if an exercise gets too high or low to be sung comfortably. But before dropping out, try three things:

1. Modify the exercise to make it easier (ie: sing on a lip trill, hum or NN/NG instead of an open vowel or other syllable, if that's more doable). 

2. Sing most of the exercise, and just "think" (audiate, or sing in your head) the pitches you can't reach without straining or going sharp/flat. This gives your vocal folds an opportunity to still adjust and prepare to sing those out-of-reach pitches, even if just air comes out. 

3. Make sure you're shifting registers when necessary. For example, you may be unable to sing higher pitches because you're still in chest voice, in which case you'd need to "shift gears" and find your head voice placement.