Explanation

Box 1: Yes
There are different replication options available with a storage account. The 'minimum' replication option is Locally Redundant Storage (LRS). With LRS, data is replicated synchronously three times within the primary region.
Box 2: No
Data is not backed up automatically to another Azure Data Center although it can be depending on the replication option configured for the account. Locally Redundant Storage (LRS) is the default which maintains three copies of the data in the data center.
Geo-redundant storage (GRS) has cross-regional replication to protect against regional outages. Data is replicated synchronously three times in the primary region, then replicated asynchronously to the secondary region.
Box 3: No
The limits are much higher than that. The current storage limit is 2 PB for US and Europe, and 500 TB for all other regions (including the UK) with no limit on the number of files.
References:
https://docs.microsoft.com/en-us/azure/storage/common/storage-account-overview

Explanation:
Box 1: No
The price of Azure storage varies by region. If you use the Azure storage pricing page, you can select different regions and see how the price changes per region.
Box 2: No
You are charged for read and write operations in general-purpose v2 storage accounts.
Box 3: No
You would be charge for the read operations of the source storage account and write operations in the destination storage account.
References:
https://docs.microsoft.com/en-us/azure/storage/common/storage-account-overview
https://azure.microsoft.com/en-gb/pricing/details/storage/blobs/

To migrate to Azure and decommission the on-premises data center, you would need to create the 5,000 user accounts in Azure Active Directory. The easy way to do this is to sync all the Active Directory user accounts to Azure Active Directory (Azure AD). You can even sync their passwords to further minimize the impact on users.
The tool you would use to sync the accounts is Azure AD Connect. The Azure Active Directory Connect synchronization services (Azure AD Connect sync) is a main component of Azure AD Connect. It takes care of all the operations that are related to synchronize identity data between your on-premises environment and Azure AD.
https://docs.microsoft.com/en-us/azure/active-directory/hybrid/how-to-connect-sync-whatis