I want to transfer all my files from my 2gb SD card to my new 32gb SD card, is it ok to just copy and paste everything from my 2gb SD card to the new one? Will it affect the apps installed in the SD card? Or is it the only way to transfer or there's something I have to do so that it won't affect my apps or whatever?

HI ... Just read carefully...
In android OS... there are two folders in memory card
1.
.android_secure - This is a hidden folder and can only be seen in mass storage mode. this contains all the data of the applications stored on memory card.
2.
Android - this is not the hidden folder and contains few data about the applications installed on phone.
Whenever u want to transfer data from one memory card to other just connect ur phone in mass storage mode and copy these 2 folders in the new card. Just make sure the new card is connected through the phone and not from some card reader. All other stuff can be simply copied in new card. After u do this ur all applications whether they were in phone or memory card will work fine and ur phone is now equipped with a new memory card.I have done this on my Sony Ericsson Neo V and its working brilliantly.