considering first question as a base: If I do not have any Transaction and as per schedule if Transaction Log Backup job run will it create any Transaction Log Backup files and can I skip those files, if there are not any transactions
Yes of course it will create a transaction log backup file. backup job has nothing to do with whether any activity is going inside database or not. Even if DB is idle with almost nothing going inside it still if you have schedules log backup it will execute.
You should not skip any files because log backups are connected with each other using LSN( its really difficult to know when actually server is idle like pointed by Kin that you might be able to skip log backup) and if you miss a log backup file restore sequence will break. So you need to make sure you have all trn log backup files intact for restore as per RPO and RTO. If you miss log file backup there could be limited restore and hence data loss.
For second part of question. You can anytime follow the restore sequence like first restore full backup then all subsequent log backups. If transaction is committed before backup finished it would be there in backup files.