If my SSD on my Air is almost full, will it slow down the computer?

The OS needs free space for a variety of dynamic files created while running. At least 10-15% should remain free to prevent stability and slowdown issues.

Yes, you will start noticing a slowdown. The OS will have to manage the free space much more intensely, getting by with less. Especially with applications that create "scratch disks", like photo and video editors.

According to Apple documentation, you need at least 9 GB of free space on the startup volume for proper operation. The statements sometimes made on this site that you should keep some percentage of space free are not based on documentation or on evidence.

Rule of thumb tends to be that you should set aside 10% of disk space for SSDs for the best speed. This comes from SSDs in Windows PCs, where the SSDs do perform more slowly when full rather than having some free space. This is just how SSDs work, which I won't get into the technicalities of. The SSD controllers themselves allocate set a reserve space (this could not be true in Apple's case, depending on what chips they use), but generally the more free space the better. So 64GB should set aside 6GB, 128GB should set aside 12GB, and 256GB should set aside 25-26GB.

SSDs technically will never be as fast as when you first got it. They slow down as soon as you start to write data to them, but the slowdown will be negligible. It's still faster than a HDD at the end of the day.

For OSX always reserve at 20GB to 25GB for the OS to do its job efficiently no matter what the size of the drive is. The OS itself takes about 10GB so that means keep another 10GB to 15GB for the OS data space -- temp files, the swap space, caches, and other transitory stuff.

This is not windows, and if you leave only 6GB free on a 64GB boot drive you are headed for performance trouble sooner rather than later.