Supposing I invented a machine that could slow down time in the rest of the universe but keep normal time for me.
Could I live in such a universe?
My machine can alter the rate of time passing and as I slow things down I guess the air will become thicker, go slow enough and walking will feel like your underwater: but how much can things slow down and still let me breath slow air?-getting it into my lungs and then round the body.(I can always wear a spacesuit so I could breath).
Could I eat slow food as their molecules will react slower inside me?
Light will become redshifted but will the actual speed of light remain the same?
Redshift enough and visible Sunlight will become microwaves, a hazard?
What will happen to my body as slowed cosmic rays pass through it?
Will the air/ground friction caused by walking make me hotter: would my shoes get red hot and my trousers catch fire?
It’s your universe fantasy.
You can make your own rules.
Seriously, how can one honestly answer your questions using the known laws of physics against a hypothesis of something not possible under those same laws?
I will offer this observation. At what point do you draw the line between the slowed down universe and yourself? Sure, wear a spacesuit to physically separate you from the universe. You still have a defined border where your spacesuit (presumably existing within your time/space continuum) physically comes up against the other time/space continuum. Care to explain how this would work?
And then somehow when you need food you grab it from the universe and bring it within your space suit to consume, does the food “come up to speed” for you?
Of, course, the scientists on the SDMB might be able offer some real proof in answering your questions.
Then again, is it time for your medication about now? 
It’s time for a beer!
The thing is I’ve seen this scenario on TV and films as a kid.
I seem to remember an old Star Trek episode where Kirk became speeded up for some reason.You know the thing, walk around while the rest of the crew are statues, etc.
I know its fantasy but it seems too easy: as I said surely the air would thicken up.
There is an old H.G.Wells story called “The new accelerators” which involved some sort of drug that literally speeded up your reactions so you moved terrifically fast, other people became statues and one of the experimenters trousers started to smoulder through air friction.