Yes your completely normal ! I'm a type 1 as well and I've never been on a diet or anything odd like that ! My diet is good as well and I don't often change what I eat because of the diabetes !
Can't see anything wrong with that. I was advised to not have a specialist diet, I can eat what I want as long as I remember to do my insulin. None of that diabetic chocolate or sugar free stuff for me! I always eat in moderation and I think that is key, don't change but always keep in mind about your levels and sugar amounts.
As for your levels, 3.5 is quite low. That's borderline hypo for me, but again that's me.