"如果实话说就怕那家公司知道目前公司的经营状况" -- This is really not your concern at the moment, your next job is much more important. After all, when you leave the current company, you will have zero relationship with it.
"申请前问了老板可不可以申请" -- This is absolutely un-necessary. Your current company is kicking you out. Your first and only priority is to find next job. When you are out, your current company will not provide money for your living. It is you to get the income. So no need to get the consent from your current boss to find another job.