I always ask.

As a customer, I don't give any weight to these badges because I've known startups that have lied about them.

As a product owner, I see multiple benefits to ask for it:
* talk to your users: you will always get something out of it
* turn a badge into a testimony
* turn customers into advocates: some customers will be willing to be contacted by your prospects (this may not apply to what you are selling)
* get better resources: sometimes the logo is not easily available in the best possible format for your use case
* avoid trouble: some companies are very careful about how their name is used, and your users might not like it if they discover the logo of their company when they know to be the first users there
* be nice: it's a basic courtesy, you will use their name for your benefit, be transparent

My experience is that most of the time, people will be happy and even flattered if they truly like your product. And you could end up with a sweeter deal than just a logo.

In order to add badges for social proof, do you reach out to these companies and ask for permission or did you say fuck it and added them once they used your app?

I think it depends if your company sales/signup is B2B or B2C (or low touch B2B). I think the prior you always make sure your contract with the company allows for it or you ask them. For low touch B2B/B2C I don't know but I would expect you can probably get away with adding them for social proof without asking and then removing them if that company requests it

It depends on the situation.

You mentioned "as seen in". In the case of the media writing about your product, it's generally fine to add their logo and link back to the article, etc. They will expect that to happen and I have never heard of anyone objecting to it.

As for showing customers' logos, I'd lean towards asking them for permission. You wouldn't want to risk damaging a relationship. If they are okay with it you might even get a testimonial out of it too. If they aren't okay with it, it's better you find out now and avoid any issues.

Where it gets a bit more tricky is when you've got some employees of a big company like Apple or Google using your product, but without the company itself being an actual customer. I've seen plenty of startups state "used by people at Apple" and I'm pretty sure they haven't asked Apple for permission, nor would they ever get it.

I think those situations are a bit of a gray area. Those startups might be telling the truth, but there's no real affiliation with Apple which in a way they are suggesting. So in these cases I think it really depends on the context, how you present the logos, etc.