On “zu” and “um zu”

Hi there,

 

I’ve learnt about sentences with ‘dass’ and ‘zu + infinitive’, but I still don’t feel so confident writing arbitrary sentences that I make up myself. I’ve read the stuff on your site too and this helps loads (much more than many of the boring grammar books); but am still having trouble.

As I understand, it’s okay to write things like, “I know I eat many apples”, in two different ways:

Ich weiss, dass ich viele Äpfel esse.
or
Ich weiss, viele Äpfel zu essen.

But are they really the same? The literal English translation is slightly different:
I know that I eat many apples
vs
I know to eat many apples

Also, I was wondering what is possible to make up the main bit of the sentence (“ich weiss”), not the dependent part. Can it just be anything that can be / needs completing? E.g.,

The sausages, …
On Tuesdays, …
I hope, …

For “I must have forgotten it”, would that be:
ich muß es zu vergessen haben.
ich muß haben, es zu vergessen.

 

(Originally asked by Edd)