Hi Mats,
First of all, this is a great start, especially for someone new to Photoshop! I'm impressed. Not sure if I'm nearly expert enough to answer your questions, but I'll give a stab at some of them.
Those circles are awfully close together! I'm guessing your planet it somewhat colder than Earth. It's a little hard to get a good sense of scale here, as I'm used to seeing equators as straight lines in most map projections. As Hai-Etlik said, it looks like you're using some sort of
equidistant conic projection, such as what we use for the US. It may be helpful for you to try sketching some sort of version of your world map (even if it's just this continent for now!) and putting it in an app like GProjector to see how this would compare to the US in size. Anyway, if that upper semicircle really is the Arctic Circle, then is it realistic to have forested areas above it? On Earth, the treeline ends well south of the Arctic Circle.
If this really is a US-size continent, then I'd recommend making your mountains somewhat more complex- if you look at a map of the US, you'll see that big mountainous areas like the Rocky Mountains are actually broken up into dozens of smaller mountain ranges rather than a single cordillera like you have here. So in an area this big, you'd almost certainly have valleys and even plains in between mountain ranges. That said, I rather like the style of mountains you have so far, though I'd recommend making them smaller and more frequent.
As for style, I like the pine trees you have (though some of them are a little fat and/or irregular), but I'd recommend drawing them smaller and having more of them (I guess that's a trend here!). It's a little more time consuming, but when they're this size they look a little awkward when I view the map at full size. I'm not really convinced by your style for deciduous forests- but that's also one of the hardest landforms to get right (in my opinion), so I don't know if I have any tips for how to improve them.