Learn English – I could not enter through the door so I was forced to climb …. a window

"Out of" and "from" mean the same thing in that context. There is no right answer. And yes, it is ambiguous whether he took the lock or the keys from the bag. One would assume keys, because who carries a lock around in a purse? However, another issue is that you don't put keys (plural) into a lock, you put a key (singular). That adds to the confusion/ambiguity here because "it" is a singular pronoun.

out of and from are pretty much interchangeable, when you are talking about materials something is made of, or an abstract concept that is derived from some thing or activity.

With is not quite the same, as it suggests adding something rather than deriving something. You could not, for example, say

I get a lot of enjoyment with teaching - not natural

but you can say

Birds make nests with branches or twigs.

because the birds are adding twigs to the nest, rather than for example shaping a twig to make a nest.

Someone had torn several pages out of her diary

In my opinion, this sentence uses the the compound verb tear out. You could use from, but the original version is much more specific.

tear out means to remove something completely by pulling hard, for example you can talk about somebody tearing their hair out.

On the other hand, tear means to pull apart, or to pull pieces off. So,

Someone had torn several pages from her diary

could mean:

• somebody pulled the pages out completely
• somebody pulled the pages apart, ripping the pages into small pieces
• somebody pulled pieces off the pages, for example ripping off the top corner from each page.

You could, of course use from together with tear out, like this:

Someone had torn out several pages from her diary