Papyrus's personality remains mostly the same, staying merciful, optimistic and confident in both himself and others. He still has these traits, but they are pushed by Gaster, specifically his mercy. He always hopes Gaster will accept mercy. Just like Gaster and Sans, his eyes glows depending on the mood, it can be purple when his fearful, it can be green if his happy and so on.
He is very attached to Sans, but their bond can break. Instances of this are found when hurting Sans' feelings because he tried to show mercy to Gaster, or his color cube he worked hard on and Sans 'ruined it' ( Sans did fix it later. )
Before the plates
Gaster did not add the Plates screwed into the brothers' hands until some time after being let out of the M-D Solution.
One of the first things that happens to Papyrus after being let out is his arm coming off. He panics and he starts to scream, which alerts Gaster to see what's going on, and after a little bit of anger, he got Papyrus's arm back on. Papyrus constantly looks for attention from Gaster, but is rejected.
The next major thing to happen is when Sans and Papyrus interact for the first time. Gaster was clearing out boxes with Sans sitting nearby, within earshot of Papyrus. They quickly realize that their nearby and start to make 'animal noises' at each other. But soon they began to babble bits and pieces of things that Gaster had said to them. Gaster decides that they are sentient after all, and that his experiment isn't a total faliure. This throws Gaster into a short panic before he makes a plan to introduce them to each other.