You really need a floor pump with a gauge. You won't be sorry. Your local shop will probably let you try some out so you can see for yourself.

No, a decent mini hand pump should be able to do about 90 psi with no problem, 100+ for a frame-sized pump. If you have something intended for basketballs you'll never get high enough for any bike tire.

I'm surprised a gauge intended for auto tires even goes much past 40psig