Whigs became Republicans for the most part
In the North, sure, but a sizable contingent in the abandoned politics (Speaker Winthrop for example) or embraced the Democrats.
In the North I would say somewhere between 65% and 75% of Whigs became Republicans depending on the state. A number of Republicans were also ex Free Soilers or Van Buren style Democrats as well so that needs to be factored in.
In the South, 80% of Whigs would be Democrats by the end of reconstruction and many of them in leading positions within the ranks of "Bourbon Democracy" in the region.
(and their platform was incorporated)
largely incorporated with some modifications, but this assumes that the Whigs had a unified and distinct platform, which they did not hence their divisions. The bulk of Clay's economic agenda was embraced minus for instance the Bank of the United States and Republicans would very quickly embrace Gold and Hard Money (Grant and Hayes, with Harrison representing a short term deviation from this stance), in contrast to the soft money stance of the Whigs.
The Whigs also favored selling the land in the west to speculators, while Lincoln's program of giving the land to homesteaders was much more Jeffersonian/Jacksonian and much more egalitarian.