Klopp has always eased in his new players, just look at Van Dijk and Robertson. So I don't know what point you're trying to make, especially with respect to Keita who didn't even have a decent run of games before he got injured.
Van Dijk played 90 mins 4 days after signing against Everton, suffered a thigh injury for the next game and played in every game after this (other than Huddersfield).
Robertson was eased more in but still played 90 minutes in games since August and September in 2017
Not sure what you are talking about. You should know these things as a Liverpool fan.
Left out of the selection against Burnley, and didn't make his PL debut until January 22nd, almost a month after he was acquired (didn't even make the squad for the 4-3 game against City). Second game after his first start in the PL, he was on the bench again against Huddersfield.
His first start in general came in the FA Cup against Everton in which he scored the winning header.
The Burnley game was on the 1st of January. Would Van Dijk even be allowed to train before this? It would have been risky for Klopp to play him on the day he officially signed.
He missed the City game because of thigh injury.
Van Dijk literally missed only the Burnsley game which is the day he signed, the City game which he was injured and the Huddersfield game in which he was rested. He also played against Swansea 90 minutes on the 22nd of January.
That is not easing someone in.