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

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'?

Probably 2 weeks.

As soon as you know how to write your value proposition

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.

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.

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.