A few things
A lease is almost never the same payment as a buy. Thats the whole point of a lease; to get into a car you CAN'T afford. A purchase of a 3 series (lets say 40k) for 72 months with 0% (which is NEVER for 72 months on BMW, usually 36) is 600/month; 750 with interest. A lease of the same car usually is somewhere in the 450-650 range depending on the lease deal. BMW has 328 lease deals for like 350-400/month right now, easily a 500+ car payment on a purchase.
My dad leased a 2005 S4 (52k) for 39 months, 15k/year, 0 down for 600. 0% for 72 would have been 770/month.
Also, you can change the mileage however you want. You don't have to stick to their 10 or 12k usual annual mileage. It usually adds 10-20/month for every bump up (10, 12, 15, 18 etc).
You most certainly can mod a lease as well. Just save the stock parts, and then sell the aftermarket ones when finished. You might loose the money on the chip (like i did on my A4, but its worth it).
Audi hasn't had good lease deals on any of their cars (compared to BMW and Mercedes who subsidize their leases, Audi doesn't) since early 2005.