You're in pretty good shape if those are the results you're getting on logic games only a few weeks in. I think more practice will get you where you want: taking timed sections, retaking those sections timed or untimed, and reviewing your results.

A trick that I have found helpful to get perfect scores on games with time to spare is to be bold and decisivie in your answer choice selection. If you diagrammed correctly, then have faith in your work and select the correct answer once you spot it. Do not spend a second more testing any of the other answer choices since they are wrong simply because of the fact that the answer you selected is right. This tactic should help speed games up to have time be less of a constraint.

Q13 is one of those questions where the answer lies just a line or two down from where you think to look. Always think that the LSAT writers will bait you and hide the correct answer almost in plain sight in these types of questions. It's almost like a taunt.