Few Questions About My Saxo Vtr?

1. When i put my car into neutral it goes to 2 thousand revs automatically. But it never used to do this at all. It does have a new air filter on it but it never used to do this...

2. The car seems to wobble a little excessivley and can at times make me lose a little bit of control.. Would this just be the tracking ?

3. And finally (this seems to be quite common with my friends too) When i go to start my car in the morning it will always not get enough power and end up cutting out within 10 secs of me turning the key.. is there anything i can do about this i.e change the battery or something ?

Any help on these would be fantastic!