First part hard yes, but that's actually explicit in OD&D. The slow adventuring pace in the dungeon accounts for probing etc.

Last part hard no, you just need to get more creative with obstacles. Like "traps" don't have to be hidden pitfalls. They can be wizardly match stick puzzles of doom and so can a 10 foot pole be incorporated into the puzzle by delicate magical manipulation by a magic user giving you a free move?

I'm not very creative, I just steal from media I like, but the sky is the limit when you stop playing character sheets and start playing the characters that the sheets abstract the wrote bits of.