Yes, most can get into a residency immediately after medical school. Now, whether that residency is your top choice of specialty or in the location you really want to be in is a different story. Some unlucky ones take preliminary medicine or surgery spots while they reapply for their desired specialty since they didn't match the first time.
Yes, if you're a US medical student. A small number might (deliberately) opt to do research for a year to make themselves a better candidate for a more-selective residency. And a very few do the same due to a failure to match or SOAP. I know of one who took the year off to have a baby.
(SOAP is a backup system for getting a residency if one doesn't match, results of which are known at the same time everyone else knows where they'll be going).