I had bought my 05 MCS about a year ago, now I just reset the ECU and changed the engine and transmission oil, the car runs great, and to gain more benefit and give the power train a fresh out, I want to also replace the air filter

should I go to cone type air filter or just the OEM flat filter?

if I go cone type filter, do I need to change the air filter box or not?

 

Welcome aboard. If you want more supercharger noise go with a cone filter. IF you just want it to breathe better go with the panel filter.

Some require you to remove the box and others you only remove part of it like on the K&N http://www.knfilters.com/air_intake/mini_cooper.aspx

 

Generally a cone filter needs a modification....the dinan cai reuses yhr lower box, and comes with a new filter and fitting.
Just removing the box and installing a cone is a hot air intake (hai), installing a filter in a box with ducting is a cold air intake (cai).
Both are mostly for sound, as the gain is about 2 hp.....bet you can get a panel filter, aftermarket that will do that, but cone filters DO help the sound of the sc come through, and dresses up the engine bay. Some can make (imo) too much whine for a longer trip, but are great around town...so look closesly at you options.

 

If your planning on doing an intake later just save your money now and get a ddmworks intake later.
You can't put a cone filter in the stock airbox, but you can put a high flow panel filter in like our dry flow filter or a K&N filter. both will give you a little power but don't look for monster gains from that.