"I bought many colored pencils."
There's no perfect rule for this. The emphasis changes depending on the placement, but you'll still likely be correct or at least understood.
I put the sentence like this: たくさん色鉛筆を買いました and it passed as correct. I am here for the word order as well :)
"Many-colored pencils" vs. "many colored pencils".
Fun to think about, thanks!
Because は is the topic marker and, in this case, you are the topic. It's implied: （私は）色鉛筆をたくさん買いました。
I think you should be able to use it -we are talking about what we bought. However, it sounds a little sloppy. You should use を for the direct object.