Restore SQL Server DB without transaction log

The transaction log is an integral part of the backup. You can't tell SQL Server to ignore the transaction log, because there is no way to let's say restore and shrink the transaction log file at the same time. However, you can take a look at DBA post to hack the process, although it is not recommended at all

Alternatively you could try some third party tools for restoring, particularly virtual restoring process that can save a lot of space and time. Check out ApexSQL Restore, RedGate Virtual Restore, Idera Virtual Database.

Disclaimer: I work for ApexSQL as support engineer

No, the transaction log is required.

Option 1:

An option may be to restore it to a machine that you DO have enough space on. Then on the restored copy change the logging to either bulk logged or simple, shrink the logs, do another backup operation on this new copy and then use that to restore to the target machine with the now much smaller transaction log.

Option 2:

Alternatively, perhaps the contact at the external source could shrink the transaction log before sending it to you (this may not work if the log is large due to a lot of big transactions).

Docs on the command to shrink the log file are available here.

This is really a question for the ServerFault or DBA sites, but the short answer is no, you can only restore the full .bak file (leaving aside 'exotic' scenarios such as filegroup or piecemeal restores). You don't say what "huge" means, but disk space is cheap; if adding more really isn't an option then you need to find an alternative way of getting the data from your external source.

This may not work since you have no control over the generation of the .bak file, but if you could convince your source to detach the database and then send you a copy of the .mdf file directly, you could then attach the .mdf and your server would automatically create a new empty transaction log file.

See sp_detach_db and sp_attach_db (or CREATE DATABASE database_name FOR ATTACH depending on your sql server version).