Nissan Pathfinder 2002

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Several things going on with my car and wondering whether or not it is worth fixing them...
-Since May 2013, (right after passing my emission te start. I'd pull into a gas station with no problems and then, noti=hing ): ometh=imes in the morning. Very random. It alwys starts by itself (changed the battery Summer 2013 exactly because of the same problem. One day, arrivedat destination just fine. Ealked to the store for a minutest which is compulsory in my state) I've had a "check your engine" light coming off and on. Will disappear by itself in a week or less. After checking with my dealer, it's the catalyst system. They recommend a B2 catalyst converter change
+ Do I need to do this or could I pass the emission test without doing so?

-My car sway terribly and I was told by those who take care of my tires that I needed to change the left and right rear trailing arm. Those who take care of my breaks, advise to change front and back trailing arms.
+ How do I determine how many exactly need to be changed?

- Last but not least. My car just won't start at times. Typical example. Over the Summer, arrived at store just fine. Went in and out in 10 minutes. Wouldn't start. Radio/lights comes on but nothing from the engine. I called a tow truck and while waiting, listened to the radio. After an hour waiting for the truck tried to start the car up and "Voila." I changed the battery over the Summer 2013 because of this problem. I've had the "oil cooler seal" replaced in 01/12 and the "chamber assy" and "engine control" in 06/12 and the "Bank 1 timing sensor" in 12/12.
For the latter, no idea yet what could be causing the problem.
+ Any small work I could do to fix the problem?
Just where to start?
Thanks anyone

[Towncivilian]

First, try running two 20oz bottles of Chevron Techron Fuel System Cleaner, one in a tankful for two back-to-back tanks. This may help with your P0430 code.

For the death sway, the rear trailing arm bushings are at fault, correct. There are a total of eight: two per arm, and there are two arms per side, upper and lower. Inspect all of these to see if any are disintegrated and if any arms have excessive play.
You can either have a shop press the bushings in, or you can replace the entire trailing arm assemblies; new ones come with bushings, of course.

For the start issue, ensure the battery terminals are tight (but not overly tight; too tight cracks the battery terminals and leads to unstoppable corrosion) and corrosion-free.

Do you have more codes other than P0430? If so, post them here.

Welcome to NICO!

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Thanks! I will follow your recommendations.

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No other codes either.