Str 2003 Rumbling engine feeling when gasing On neutral between 1000-2000 rpms. No rumbling over that or on neutral below 1000 rpms. Engine mounts ?

 

Fix the other faults first.

I'm puzzled why you bought this car with the faults posted...

 

Well I really had a great deal. I'm very hookep up with the connections. It's my 10th car (4th european car). Not really worried about tiny problems. Freak of car I only have a check engine : pcm valve nothing serious or gas cap (same fault). If I erase the check engine let's say, it comes back after 4-6 days. My mechanic is the best Jaguar in Canada so even better. But anyways if you any ideas let me know. Thanks

 

You're going to need cat(s) if you don't fix air leak(s) soon.