caveat: I've not birded in Mexico... I just look at pictures in guides.
The first picture is closest to a female Yellow-faced Grassquit. The pale yellow throat surrounded by black, the pale spectacle and lores, the thick bill, the lack of wingbar: all point to this identification. However, my book shows that the overall colour of the bird would be somewhat darker. The Buff-throated Saltator has a white throat and yellow on the upper chest with a heavy black "V" on the chest. Also, the Saltator seems to have a noticeably longer tail.
The second picture certainly looks like one of the mimics. I think we can rule out the thrashers by the clear breast and the catbird by the contrasting wings and belly. The Socorro Mockingbird (formerly Thrasher) still has some light streaking on the flanks and is only found (so far as I can tell) on one remote island. The Blue Mockingbird is, well, blue. Which leaves Northern Mockingbird and Tropical Mockingbird. I can't tell from the picture which of the two it might be.