Dear Cherisse,
You can apply for your ILR 28 days befor your 2-year visa runs out. As you have delayed 2 months in your enterance, the best thing to do is applying for ILR (completing form FLR(M) ) but because of that delay, they might process your application on the basis of visa extention (3 or 6 months). However they might accept it as an ILR case, too.
If you apply in person (the way I did) in one of the public offices, you don't need to leave any of your documents there. They will take copies of them and 90% of applications are done in 3 hours (if there hasn't been any shortage in documents). Even if they process your application on the basis of extention, they won't keep your original documents. So don't worry.
Personal advice: Provide as much documents as you can to support your application and have a good and acceptable reason (excuse) for your delay. In this way you can satisfy them to accept giving you ILR rather than visa extention.
Good luck!