No, large companies are generally scrupulous about licensing patents. Infringing a patent makes it valuable, and thus worth selling to a competitor or underwriting by a venture capitalist. Nobody wants to have the billion dollar product that is enjoined from sale.
Depends. Usually big companies have cross-licensing agreements between competitors (since they usually can't do a product without each other's technologies - example: hard drive companies)
Also, it's easier for them to come up with a way of not infringing the patent in the first place.
The big company usually pays when they don't want to produce it.
Otherwise, they just do it and wait for the lawyers (who are not going to come)