Hey Mike,
Thanks for the questions, and welcome to the Forum! I'll see if I can give you some help on both of your concerns.
Speed is an extremely common topic of discussion for test takers—arguably THE most common, in fact—as nearly everyone who takes the LSAT struggles to complete the sections in the allotted time with a high degree of accuracy. So I'm happy to report that not only are you in good company with your concerns, but also that we've produced a wealth of information and insights on this very subject.
Here are several threads on improving speed, each of which I think you'd benefit from reading. And a Forum search for terms like "speed," "pace," and "timing" is likely to turn up a great deal more
A broad discussion of speed involving a few different instructors (myself included):
lsat/viewtopic.php?f=2&t=7543
Dave Killoran's advice to a student about LR speed:
lsat/viewtopic.php?f=12&t=981
A lengthy conversation between a few instructors (again, myself included) and a student about speeding up:
lsat/viewtopic.php?f=2&t=7943
A good reply from one of our instructors about moving more quickly and maintaining a high level of comprehension:
lsat/viewtopic.php?f=2&t=7678
Some additional tips by another one of our instructors for going faster:
lsat/viewtopic.php?f=2&t=7017
A blog article by one of our Developers with three tips to increase your speed:
http://blog.powerscore.com/lsat/lsat-sp ... -your-pace
And finally some advice on how to move more quickly in Reading Comprehension:
http://blog.powerscore.com/lsat/a-timin ... erformance
That's really just the tip of the iceberg when it comes to articles and advice on pacing, so again please take the time to both read the above information and do some additional digging on your own!
As for LG inferences, my go-to advice here is to always, ALWAYS focus only on elements that can be known with certainty: LG success comes from concentrating exclusively on what MUST occur and what CANNOT occur, and ignoring those situations/events that are merely possible (the COULD idea that so many people get hung up on). Of course, that's also a tremendously common concern, and as you might expect we've produce a huge stockpile of advice on inference-making, as well!
Here are some further discussions you'd be well-served by reading:
A blog post I wrote outlining exactly what I mean by "focus on certainty" when attacking Games:
http://blog.powerscore.com/lsat/bid/308 ... -Certainty
A related blog by Dave Killoran where he described how to best attack both Global and Local questions in LG (ideas closely related to inferences in your setup):
http://blog.powerscore.com/lsat/bid/308 ... Strategies
Another blog by a PowerScore Developer on recognizing Limited Solution Set games, something that I think will really help as you seek to create optimal setups:
http://blog.powerscore.com/lsat/bid/317 ... -Set-Games
A Forum thread with a few PS instructors discussing inference-making:
lsat/viewtopic.php?f=6&t=7295
Another thread discussing linkage inference in Grouping Games:
lsat/viewtopic.php?f=6&t=7350&p=18825#p18825
Again, this is such a common issue for people that we've addressed it time and time again, so please take a moment to search for key words like "inference" (or "inferences"), and the like. You'll find a ton of excellent advice that I'm sure will really help you out!
Thanks again and please let me know if what you see above and find on your own helps!
Jon