I think Maggie's answer makes some sense. Here are what I summarize.
In some cases, 'and' and 'with' can be transalted into the same meaning '和'
E.G. I went to the park with Alice.= Alice and I went to the park (together).
They both mean: 我和Alice一起去了公园。
Difference between 'and' and 'with'
AND
1. As Maggie mentions, sometimes it links two actions and it's like sequence words--then or next. It may be translated or not be translated. That's why when we foreigners' chinese articles, we may find the passage filled with too many conjunctions. E.g He ate his breakfast and left for the school. 他吃了早饭,然后去上学了。So '然后' is the meaning of and.
2. Its another meaning of '不仅...而且/还'. It links something parallel and means one does more. He finished his homework and helped with the housework. 他不仅完成了作业,而且(还)帮忙做了家务。But if you translate as follow is also ok: 他先完成了作业,然后帮忙做了家务。 Using "不仅..而且.." kind of praises one's work.
WITH
Maggie's example with 'with' is not the usage of 'with' as a conjunction but a preposition I suppose. And if used as a preposition, it doesn't have a fixed translation. See examples.
Beijing is a city with long history.北京是一个'有'悠久历史的城市。Meaning as '有'
With his help, she finished her homework. 他帮助她完成了作业。No necessray translation.
I cut up the banana with the knife. 我用刀切了香蕉。 Meaning as '用'
BECAUSE
This one is easy. It means '因为' (due to, because of,...)
So accumulation is must. You can list some puzzling sentences and it may help you understand better.