No, the capacitor is not to be in series with the varistor. Keep the capacitor where you had it before, between 15V and ground next to J3.
PaulH is correct regarding the positioning of the varistor. Keep it very close to J2, and connected directly to pins 1 and 2 of J1.
Regarding the FQP47P06 and the FQP27P06, the only significant difference is their current ratings, which are 47A and 27A, respectively. They are both 60V (or -60V depending on ones perspective) P-channel MOSFETs. Either would be fine. It appears to be correctly connected for reverse polarity protection.
If pin 1 on J3 will be in the 14V range, then your resistance is fine for the IR LED.
If pin 2 of J1 is a digital signal going to the Arduino, then 3K is probably fine, though 10K is more optimal. Optocouplers tend to have a wide range of output characteristics depending on the production lot, so one might work fine with higher collector current, while another may not. It has to do with how sensitive they are to the IR light source (the spec is the current transfer ratio, or CTR). By reducing the collector current to under one milliamp, it should give you good results regardless of which specific production lot you get.