How long before the actual launch of your product, would you launch a "coming soon" page?

If you are trying to capture email addresses on your site for a waiting list, honestly the earlier the better. You can then slowly get folks to sign up for the wait list and it is already there for you.

As soon as you know how to write your value proposition

Depends. If you want to collect leads then a launch page is good for capturing emails. If you do not require emails then I see no point in having a landing page. Either wait until you are ready to launch and then market it, or just put the product up for pre-order. A coming soon page doesn't really give me much excitement and is forgotten about 3 seconds after you leave the page. I would only end up going back if I saw marketing for it again.

Depends on what pre-launch marketing you're doing and how you're planning to acquire your first users. If this is saas and you're doing sales, high-quality landing page helps you look legit. If you have a big pool of beta users, maybe testflight is a better investment. The bigger question here is maybe 'what's your launch marketing budget and how are you planning to split it'?

I would say around 4 weeks. I do have a page, but not a coming soon page, just a page that simply explains what I am trying to build and subscription email.

Probably 2 weeks.