Have you not received any Delivery Specs? Ask for them if you have not. They should clue you in on whether or not a test tone is required. If it's just for the Mixer to import into his session then you may not need any. I work in TV and I know that all of our deliverables (Mix Stems) go out to the networks/production companies with either 1 full minute of 1k tone at -20db (00:58:30:00 - 00:59:30:00), half a minute of the same (00:59:00:00 - 00:59:30:00), or occasionally no tones at all. It's all dependent on the project or network specs and I can only assume film specs would vary in the same manner. Get the specs and clear any confusion.
As far as count-off beeps go, there is usually only one, the 2-Pop. Another 1K tone for 1 full frame exactly 2 seconds before the hour mark (00:59:58:00 - 00:59:58:01) or whatever time your project starts. There's typically a visual countdown on the film/tape, as well, so make sure your 2-Pop is synced with the 2.