Yes, there ARE dictionary that have example sentences, but this is bad because of two reasons: 1. They are often very long and there are kanji you can´t read yet. 2. The verb you are looking for is not used in the way that you want it to be used, so it´s no use reading the sentence. I´ll give some examples: ゲームで遊ぶ but サッカーをする、カラオケで歌を歌う、宿題を急いですand NOT 宿題を急ぐ.
What you really need is a good JP-EN dictionary (ideally one aimed at learners) with decent sentences.
For example:
http://dic.yahoo.co.jp/dsearch?enc=U...type=0&dtype=3
- all the example sentences here are quite short and have English translations.
おもちゃで遊ぶ
子供たちは野原で楽しく遊んだ
illustrate two different uses of で with this verb (both pretty standard uses of で)
and sentences like this show other patterns:
隠れん坊をして遊ぶ
(not 隠れん坊を遊ぶ)
Your example in English doesn't really work because, say, "I'm looking for someone" and "I'm looking after someone" are both grammatically correct, but with different meanings, and some other things could go in there (I looked for him, I looked after him, I looked at him, I looked up to him, I looked past him, etc).
Similarly in Japanese you can have things like ある所に歩く、ある所で歩く、ある所を歩く、ある所ま で歩く、ある所から歩く
Some of your Japanese examples have mistakes, e.g.:
宿題を急いです
る (no problem, I think)
宿題を急ぐ - the problem here is not that を doesn't go with 急ぐ , because it can, but more I think that "XXを急ぐ" usually has some sort of target/goal in XX, and "homework" by itself isn't a target. It's the same as in English, you can say "hurry completion" (of the project) but not "hurry project" by itself.
If particles themselves are something you have trouble with, there are specific books on the topic. A Dictionary of Japanese Particles by Sue Kawashima is quite good.