If "Backup Exec" is really SQL aware then it should be able to do a complete point-in-time recovery, but maybe you can better ask this on a forum of the Backup Exec manufacturer. Or test it of course 😎

If you create your own maintenance plan it could (and probably will) interfere with the backups of Backup Exec unless you specify the COPY_ONLY option. Each log backup taken after a normal FULL backup has a sequence to this last FULL backup as initial starting point. When you create a backup using the COPY_ONLY option, the backup doesn't interrupt the sequence of the LOG backups.

But after restoring a COPY_ONLY backup it is still possible to continue the restore using the LOG backups. Start with the first LOG backup taken after the COPY_ONLY backup has been taken.

A backup of a database is an ONLINE operation and there's no need to kill connections or bring the database offline. Users usually won't notice anything and can continue to work, unless the server is allready under a lot of stress. Restoring a database over an existing one needs that the existing database is exclusively available for the restore procedure. No connections are allowed untill the restore is finished.