The limits are unknown, mate. I guess it is random, but you should have atleast some karma and days to start with.
As for getting link karmas, there's a subreddit for that exchange but some people I know reported of getting their accounts banned because of that.
I suggest you find good funny/controversial content on social media and share in relevant subreddits to gain karma. Example - r/funny. A post there when going viral can give you as much as 5k link karma in a day.
Go for any latest news about some book, like the Winds of Winter (Even a selfie with George R R Martin, the author )and post it in r/asoiaf and r/GameofThrones and you will have 10k Karma. Heck, you could even click your (or neighbour's) cute pet's posts and post in r/aww and r/awww and r/dog and r/pets and gain a loadshit of Karma.