Are the picks free or are there CP penalties for the previous or next race?
No CPs are counted for this weekend, or next weekend.
Pick anyone you would like for the next two weeks with no penalty.
I'm a little confused on how to pick drivers

. Can someone please explain it to me?
Pick any two drivers from Friday night's Showdown race. You get some points for them if they finish anywhere in the top five of the Showdown race.
You only get to pick one driver that is already in Saturday's All-Star race, so you want to try to pick the two drivers that you think are most likely to advance to Saturday's All-Star race from Friday's showdown race. This is pretty much the 9/15/17/27/42/43, in some order.
The top two finishers in the Showdown race automatically advance, plus another driver (that must finish on the lead lap in the Showdown race) that receives the most votes in the fan vote competition. If the fan vote winning driver doesn't finish in the top five of the Showdown race, you still get zero points for that race from that driver.
There are a lot more total points available in the five segments of the race held on Saturday.
A perfect set of picks would yield the following:
First and second place in Friday night's Showdown race: 5+4 points and 1 CP. Both drivers advance to All-Star race on Saturday.
One of your three drivers wins the pole for the All-Star race on Saturday evening: +2 points.
Top three sweep in each of the first four segments: 3+2+1 points and 1 CP for each race (24 points/4 CPs total)
Top three sweep in the final segment: 5+4+3 points and 2+1+1 CPs.
For the weekend, that's a total of 47 bonus points and 9 CPs that are possible to earn (no matter how unlikely...).