Ther first one is chalkhill blue rather than Adonis. I think the chalky whiteness visible on the forewing is the giveaway, though the wing shape and general feel also say chalkhill.
The second is, as you say, common blue. The dirty fringes and overall colour scheme suggest a female. Without seeing the forewing you can rule out any of the Lysandra species (because of the fringes) and also Plebejus, because of the white wedge in ss.3-4. It's not Chapman's blue because the black submarginal spots are not clearly set in white, and I don't think it's Escher's (but I can't put my finger on exactly why - so Escher's remains sort of in the picture).