No you don't have draw such serious conclusions
Thanks for detailed description but still I need little more information.
First of all let me answer few things. Sinus arrhythmia
is by and large a normal phenomenon and doesn't generally imply disease and its in fact absence of sinus arrhythmia may suggest disease states. And it by itself it won't produce any symptoms so one thing is certain you can stop worrying about it.
Dark heavy circles again have nothing to do with your brain and generally are skin changes in response to age and stress
and generally benign and I also guess you are mixing heaviness with dark circle and heaviness is manifestation of fatigue
Coming to your dizziness
since it is present only at rest and goes away with exercise it also could be only fatigue.
But few more details:
1. Did you ever fall because of giddiness?
2. Is there hearing problem or tinnitus(sound in the ear)?
3. Do you have any palpitation
or breathlessness when you feel giddy?
4. Are there any eye symptoms like sudden darkness or double vision?
If none then you are fine and nothing to worry. If yes please get back to me with details.
Apologies if I have bored you with a long answer but was trying to make justice to your query.