You can try as many times as you need.
No it does't count as express entry application. Application is when you get invitation to apply and you submit your actual application.
Well it happens. Sometimes those requests come back in 6 months and more. Just apply again. These requests are not on the first come first served basis, so reapplying helps.
But on the bright side if IRCC asks to redo the medicals, it most likely means that your application is progressing and might be close to be finalized.
If your medicals are expired, you need to retake them, you have no choice.
Your language test results won't expire while your application being processed.