No problem I don't know of any site that pays in crypto in particular, but there are many that do for a certain crypto or a certain job. For example, steem altcoin pays for posting articles that are liked by the network. There are people or projects offering rewards every now and then for something and pay in BTC. That is usually case by case but bitsquare has some bounty rewards open if you are familiar with Java(https://github.com/bitsquare/bitsquare/issues?q=is%3Aissue+is%3Aopen+label%3A%22Bounty+task%22).
I used some faucets back in the day to get my first btc. Took me a lot of time to get small amount, even tho the price eventually grew. I don't really want to recommend any, because it would probably take you 2 whole days of clicking to get a dollar worth of btc, but they paid as promised till now.
And about work in bitsquare, hopefully we will be seeing this when the DAO gets going which is in the next version. Maybe we should have some promoting rewards or something like that, we shall see.
But ofc the easiest way of getting a significant amount in the btc if you have none already is to buy it at a centralized exchange, but that comes with a risk of privacy ofc, even tho just sending btc to a new address could mean to the observer you sold it already or just participating in a trade with altcoin and back would help.
I would recommend to find a person on a bitcoin forum from your local region that is willing to sell you btc in person, he/she will not ask you for any personal details obviously. Or just look around, follow some bitcoin news or forums and I guarantee you that sooner or later you will see a bounty you can grab. There was a bitsqare bounty just 3 months ago for recommendation of new name(it will be bisq), you will see them more and more, and they are not that rare on the internet.