This type of behavior can be very frustrating and time consuming. Do not give up it can be fixed.
Animal behavior changes are difficult because of the language barrier. Being consistent is very important.
Since you have ruled out any medical issues, it sounds like it is a behavior issue. Having a set schedule for feeding and sleeping is good. It sounds like what you dog is doing is separation anxiety.
A few questions?
Where is the crate located? Is it in the same room or is it in a separate room? Does you dog take a nap in the crate or only at night time or when you leave?
Having the crate located in the same room as where you spend time watching TV, relaxing while doing work allows you dog to be able to see you and still be close. Crate training extends beyond just night time or away time. Teaching your dog to be OK in the crate even in the same room take times. This can help to reduce anxiety of being in the crate when you are not in sight or away.
Adjusting how long your dog stays in the crate can also help. If you have a routine that your dog has learned such as getting your car keys can cause anxiety for a dog. If you keep your dog in the same room in the house can be an issue. You won't have any choice of how you put your dog in the crate and then get keys, etc. Changing that behavior can help. Putting your dog in the crate at different times and NOT leave. Putting dog away for a few minutes and then letting dog outside. Training with the use of a trigger word (go potty..etc) help to let them know it break time and not play time. Putting dog away and then leaving for only a few minutes and come back and let dog out to go to bathroom again.
If you know about how long it takes before your dog goes to the bathroom, adjust the time of being away for less than that time and then gradually make it longer.
It takes time and patience...