1) Will the synchronization still happens between Application and DB server ?
No synchronization will not happen during restore operation
During the DB restoration will the DB which is part of AOAG is locked out so that the synchronization with Secondary AOAG replica not happens ?
Please note that you cannot just go ahead and restore database which is part of availability group, you would have to evict database from AOAG, restore it and then add it back to AOAG see This Link. The query would look like below(shamelessly copied from This SE thread)
--on primary
ALTER AVAILABILITY GROUP MyAG REMOVE DATABASE AdventureWorks2012;
--on primary
RESTORE DATABASE AdventureWorks2012
FROM AdventureWorksBackups
WITH NORECOVERY,
MOVE 'AdventureWorks2012_Data' TO
'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.mdf',
MOVE 'AdventureWorks2012_Log'
TO 'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.ldf';
RESTORE LOG AdventureWorks2012
FROM AdventureWorksBackups
WITH RECOVERY;
--on secondary
RESTORE DATABASE AdventureWorks2012
FROM AdventureWorksBackups
WITH NORECOVERY,
MOVE 'AdventureWorks2012_Data' TO
'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.mdf',
MOVE 'AdventureWorks2012_Log'
TO 'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.ldf';
RESTORE LOG AdventureWorks2012
FROM AdventureWorksBackups
WITH NORECOVERY;
--on primary
ALTER AVAILABILITY GROUP MyAG ADD DATABASE AdventureWorks2012;
--on secondary
ALTER DATABASE AdventureWorks2012 SET HADR AVAILABILITY GROUP = MyAG;