I think you should cut down on the fat first tbh. 1 - You don't seem to feel very good at present and 2 - I don't think you'll feel any better if you gained even more weight.
So once you cut down you can then build up from a lean frame (and not overdo the bulking!). I think that may be the best course for you in my opinion.
As for the changes to diet for cutting.. you may want to post it up in the diet section for advice.. and mention that you're a vegetarian before other members jump on you lol.
What do you mean that cardio with weights may have a negative effect? Can you expand on that a bit more please as I don't think I understand what you're implying.
You can still follow the same weights routine you're doing now. If it's been over three months or you're tired of it then you can always follow another. There are many many many different ones out there. Ice_mach did an excellent job for routines... You can look here for some ideas if you like.. they're seperated into different categories: http://www.muscletalk.co.uk/fb.asp?m=854463
As for losing fat whilst building muscle.. that can be achieved, but under certain circumstances. You may be able to do this at the beginning, but the effects will definately not last long. So now, the new training will stimulate muscle growth and also bump up your lean tissue.. which will burn more calories (so would the elevated metabolism from added physical activity and better eating). So yes it can give the 'phenomenal' effect of losing fat and building muscle at the same time as your body composition changes, but in no way is it a permanent thing in most cases. The effect will wear off once you adapt to the changes so-to-speak.
So yeah, continue to eat well (make changes to it with help in the diet forum if you like), train hard, and be patient.
Monitor your progress and adjust according to your goals/needs. And you'll be ok.
Taking pictures or keeping track of bodyfat % can help monitor. BMI isn't that great to go by.. and to some extent.. neither is using the scales. Although the scales are IMO more useful than BMI and can at least give you some sense of direction.
and Welcome to MT