To answer your questions:
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Yes, you could absolutely go the cold outreach route. I think you have to be comfortable getting a lot of rejections and do a good job of qualifying leads. There are both paid and free options that would make sense IMO: LinkedIn In-Mail can be highly targeted but is also wildly expensive. You could also use a tool like Apollo.io. IMO the downside of cold outreach for a B2C product is that it feels kind of gross.
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There are tools that scrape ads and then aggregate them based on the advertiser. They are not free though and they can be pricey.
The exception would be the Facebook Ads Library. Moat used to have a free ad search but it looks like Oracle got rid of it after they acquired the company. You could also try SEMRush which I believe has some functionality for free.
As an aside, what justifies your current pricing? Is your tool $19 better than the free options I was able to find?: https://www.lightxeditor.com/photo-editing/linkedin-profile-picture-maker/
Yeah don’t use them.
You’d be better to just use Apollo.io and do the work yourself.