It should however be noted that "åka" can be used in a more general sense when going somewhere far away (no matter the mode of transport). It's more common to say "Jag ska åka till Thailand" ("I will go to Thailand") than "Jag ska flyga till Thailand".
It's fine to say "åka" even if you're the one driving the car. "Jag åker till Stockholm i morgon" can be used if you're taking the bus, a plane, being a passenger in a car, or driving yourself - unless you want to point out that you're driving. Compare with "I'm going to Stockholm tomorrow" and "I'm driving to Stockholm tomorrow".
Yes, but in Swedish you can use the present tense to refer to the future, whereas in English I would only use the present tense to refer to the future when talking about bus and train schedules and such. Otherwise, I would use 'will', 'be going to' or the present continuous. I am not a native speaker, though.
This is how I've learned to use the future tenses in English:
The present simple can be used about scheduled events, such as bus and train tables, for example, "The train leaves at 2 o'clock."
"He is going away tomorrow" (present continuous) would be fine, but "He goes away tomorrow" still sounds wrong to me. Perhaps you can think about it as a scheduled event, though?
I was replying to your original post, sorry about the confusion. And yes, the present continuous would be better here. "He goes away tomorrow" does sound wrong. (Present simple is possible in some cases, like the ones you pointed out, and some others, but you're right, this isn't one of those cases.) However, in Swedish (based on what we've learned so far) there is only one present tense. So while we could discuss what's wrong and what's less wrong and what English textbooks say... for the purpose of learning Swedish it doesn't really matter. :) There is one present tense, which happens to translate 2 ways into English. As long as the "correct" one is accepted, having the other one doesn't hurt anybody. :)
You could also use skrinna instead of åka skridskor. I thought it was a regionalism (fellow Finn here...), but SAOL (http://www.svenskaakademien.se/svenska_spraket/svenska_akademiens_ordlista/saol_pa_natet/ordlista) just lists it without any comments regarding specific usage.