Q1 Is there a way to execute a DELETE statement with a WHERE clause (cannot use TRUNCATE TABLE) without logging?
A1 No. (Not in any kind of production setting. Also, note that truncations are not logged on a row by row basis.)
Q2 Is there a way to execute a DELETE statement with a WHERE clause in order to execute a "faster" deletion of records?
A2 Sometimes, yes. Generally optimizing large scale deletions involves on the data, indexing, the schema, and the environment. Sometimes it is a matter or having a suitable index the system can take advantage of; sometimes it may be a matter of reducing concurrency locking issues; sometimes it may be a matter of dropping excessive indexes (and later recreating needed ones); often several such factors may be involved.