What happens to the bitcoin mining if the device changes? First I've opened this site via mobile and registered with a Google account. Some time later, I continued to mine bitcoin through my laptop with the same account. Will this device change make it impossible for me to exchange the earned bitcoins to dollar or other currencies?
Will this device change make it impossible for me to exchange the earned bitcoins to dollar

No, it will make no difference whatsoever to your ability to exchange earned bitcoins to dollars.
However this is because all websites offering Bitcoin mining with mobile phones or laptops are scams which have no intention of ever giving you the Bitcoins they have tricked you into thinking you have earned.
Criminals don't care what changes of computer their victims make.
They might use it as a convenient excuse to blame you for not being able to give you your &quot;earnings&quot; but they'd have easily invented some other excuse if you hadn't made any change.

As others have noted

The difficulty of mining Bitcoin has increased hugely year on year.
It became infeasible to mine Bitcoin on laptops many many years ago. You now need nearly-free electricity and the equivalent power of tens or hundreds of thousands of laptops to have any chance of profit.
It has never been possible to mine Bitcoins on smartphones.