How to recreate an Index with the same settings?
You should probably play with scripting options in Tools-Options-SQL Server Object Explorer-Scripting in SSMS menu.

There you can define what you would like to script and what not. Compression is there.

As for the other properties - have a look at this StackOverflow question - it will probably shed some light:

SORT_IN_TEMPDB is not a property of an index, but rather an option that you can specify that says how the index is created. Once the index exists (i.e. the create index statement completes), whether or not SORT_IN_TEMPDB was specified at creation time isn't stored anywhere because it doesn't matter.