Kent is saying that he thought the King was going to give his power to Albany rather than Cornwall, Gloucester agrees and says, it appears not to be that person he values most, but both are an even match and he is unsure who the king will give it to. I cannot see any motives from either speaking character here.

Kent is asking if Edmund is Gloucester’s son, which he is, Gloucester feels squirmish when admitting but is getting more comfortable with it. Kent I believe is possibly having a dig a Gloucester, however, he motives are not harmful, just to maybe remind Gloucester of his past, possibly trying to point out that he is above him

He wants to split his kingdom amongst his daughters, however specifically he has already decided that he wants to give it to Cordelia. If this part King lear is saying, that it is his intent to divide the kingdom between his daughters and to relieve himself of duty due to his old age, and use the youth of his daughters to do the job. While he prepares to die and enjoy his lasting years. His motive here is very selfish and he is only doing this because he wants to be able to enjoy the label of being king but not have to have the responsibility.  

This gives away Lear’s affection for Cordelia because he says “more opulent than your sisters.” Opulent meaning wealth or luxury, meaning can she produce a better work in order to tell her father how much she loves him. He is saying that