1. 怕你一家吃不下
Here 吃 does not simply mean eating, instead, it is more complicated and derived from eating.
It actually means that someone tries to tackle a problem or take control of a situation and then get profit from it. It's just like "eating" the profit.
So here 怕你一家吃不下 means that the speaker thinks you might not be able to control and manage all the things solely, and the speaker is suggesting coorperation to get profits.
An interesting thing is that food in Chinese has a lot to do with profits. Like: the 油水 in 这里很有油水 means a lot of profits; and the 骨头 in 家装市场这块骨头不好啃 means profits, which is usually difficult to get.
2. 吃老本儿可不是长久之道
Here 吃 means consuming or living on something which I think is also derived from eating. 吃老本儿 means living on or rely on one's past gains.
Example:
你应该继续学习而不是吃老本
You should go on studying instead of resting on your laurels.
So 吃老本儿可不是长久之道 means that you can't live on your past gains for a long period of time.
In addition, the 吃 in 坐吃山空 has the similar meaning with the 吃 in 吃老本