To show all backups of a Database in MSSQL you can use the following snippet.
This snippet will show you every path even if the backup does not exist anymore.
SELECT Distinct physical_device_name AS [BackupPath] FROM msdb.dbo.backupmediafamily
To list last backup date of all databases in MSSQL you can use the following snippet.
SELECT db.name AS [Databasename], case when MAX(bck.backup_finish_date) is NULL then 'No Backup' else convert(varchar(100), MAX(bck.backup_finish_date)) end AS [DateOfLastBackup] FROM sys.databases db LEFT OUTER JOIN msdb.dbo.backupset bck ON db.name = bck.database_name AND bck.type = 'D' WHERE db.database_id NOT IN (2) GROUP BY db.name ORDER BY 2 ASC