How would enabling FileVault alter my system and TM performance? What are the pros and cons, performance-wise, of enabling and using FileVault? Is there any at all, or does it slow a computer down significantly or on the contrary speed it up? Also, what effect will it have on Time Machine-backups (performance-wise)?
CPU load
Filevault 2 supports Intel® Advanced Encryption Standard (AES). It's important to know if your Mac has an Intel processor which supports this, as it significantly reduces the CPU overhead. Search for you CPU here an look if is supports the New AES instructions.
My Macbook Pro 2011 got this feature enabled via a firmware update (Apple did not enable this with the newly shipped MBP). With AES encryption acceleration, the performance drop with Filevault 2 enabled is almost unnoticeable during normal usage. The maximum read speeds of my SSD only dropped from 510MB/s to 490MB/s.
Ars Technica, published an extended review on Filvault 2 in Lion. They say:

Apple also leverages the special-purpose AES instructions and hardware on Intel's newest CPUs, further reducing the CPU overhead. The end result is that regular users will be hard-pressed to notice any reduction in performance with encryption enabled.

As the overall CPU load is nearly unchanged, the battery life is not affected significantly.
Time Machine Backups
If you backup up wirelessly (unencrypted) or locally (encrypted, USB) the performance of Time Machine will not be affected significantly.

First, because the of the AES acceleration mentioned earlier.
Secondly because Time Machine creates local backups (snapshots). OS X Lion compensates for the potentially unavailable external disk by keeping an additional backup locally on the primary hard drive. This has its obvious advantages, since you can restore to past Time Machine backups right away from anywhere.

I've been using Filevault 2 encryption on a MBP 8,2 for three months.