Can i able to link/sign in with the basic dropbox acount to the app created using "dropbox for business app's console" ?

Apps that use the Dropbox for Business API can only be linked by Dropbox for Business team admins. A user with a Basic account will not be able to link with a Dropbox for Business app.

Q: If so, once after the dropbox for business team admin finished linking to the app that uses the dropbox for business api, then can members of the dropbox for business team able to sign in with their account to access the files to perform uploading and downloading of files from the app using the core api calls? Thanks.

Dropbox for Business apps aren't used by individual team members.

If you just want to use Core API calls on individual users, you shouldn't create a Dropbox for Business app.

Thanks. Q: Dropbox for business app is linked by signing in with a business team's admin account. Then, what is meant by "member file access" mentioned in the dropbox for api in developers tutorial? Is it mean, by using the api calls, can we able downloading/uploading files from/to a team member's account via the app which is linked with the admin's account?

If so, whether the member file access is limited to only the files in the shared folders and the team folder or we can able to download/upload all the files and folders from the team member account through the app. Please clarify me the doubt and guide me if my question was wrong.

Yes, a Dropbox for Business app with "team member file access" permission that has been linked by a team admin can read and write all files for all members of the team.