She is VERY young, I would not expect her to be house trained before 5 months and not 'reliable' until at least 6 months.

And eating, oh yes, poodles eat very little, but often! Don't start hand feeding her or you will make it her habit and you will be stuck with it. Just feed her 3 times per day at this age. Put the bowl down, leave it for 10 minutes, then pick up until next meal time.

Remember: if you do something once, and they like it: IT IS A RULE!