Some of the time crossover is caused by bringing the arms around in an arc during the recovery phase instead of picking up each arm by the elbow and tracking the elbow forwards. If your hand isn't hanging from the elbow but instead is swinging wide, the momentum will carry your hand across your center line once the hand enters the water. You can fix this by doing drills like Fingertip drag (drag your fingertips forward through the water during the recovery phase of each stroke), the Shark drill (picture your elbow rising up out of the water like a shark's fin in Jaws), or the Zipper (bring your thumb up the side of your body during the recovery phase of each stroke). I tell my swimmers to picture themselves like marionette puppets. At the end of each stroke, your puppeteer picks up your elbow by a string and moves it forward in a straight line past your head. Your wrist and hand merely dangle from this elbow until they enter the water in a clean straight line in front of your shoulder.

For the kicking, do you mean a bigger kick as in straight up and down, or are your legs scissoring to the side? Are you kicking using a 6-beat or 2-beat kick? (2-beat is one kick to each arm stroke, 6-beat is 3 kicks to each arm stroke). I'm guessing a 6-beat kick if you're giving a stronger kick once every 6. As long as you're not overbending your knees or scissoring out your legs wide, it's probably not too big of a deal to have one strong kick, but personally I try not to kick much at all in distance swimming and use a pretty gentle 2-beat kick. Anything extra you're putting into your legs uses up a lot of oxygen, so you might try kicking less in general if you find that's an issue.