Will I be able to expand Synology later without losing data with regular RAID

I think you've got it right. Make sure you understand and heed the warnings regarding growing RAID 5 in man 8 mdadm.

Personally if I were growing an LVM volume, I would not be growing an existing RAID array to do it. I'd create another RAID array, create a new physvol from it, and add it to the same volume group. This is a much safer operation (doesn't involve rewriting the whole RAID5 array across the new set of disks) and keeps the size of your arrays down.

Instead of a single boot disk and 3 disks in RAID 5, consider 4 disks in RAID 10. This is both faster and safer. You do not want your NAS to go down if the single boot disk fails. Additionally, RAID 5 has poor write performance and does not rebuild reliably on large, terabyte-denominated volumes, especially when you are using inexpensive drives.

Answers:

1. Replacing a disk with a larger one: Not with a standard RAID controller. Some vendors (e.g. Drobo) have proprietary RAID implementations that support adding disks of dissimilar sizes, etc., but traditional RAID remains far more dependable. If you want to play with something dynamic and innovative, I would suggest ZFS. Added in response to TomTom's observation that only half of question #1 had been answered: Expanding an array by adding disks of the same size as existing array members is supported by many enterprise RAID controllers. Larger disks will be treated as though they are no larger than existing disks. This may be unsupported by low-end/integrated RAID devices. Check the documentation for your specific controller.

2. No. RAID is never an excuse for failing to have a backup and a DR plan. Having "too much data" is also not an excuse for failing to back up; however, it may be an opportunity to assess whether any significant portion of your data can be classified as genuinely unimportant.

3. With consumer grade 2TB SATA drives costing only $80 each in 2011, and enterprise-grade 2TB SAS drives costing only $240, you can add 4TB of usable RAID 10 capacity for $320 (consumer-grade) or $960 (enterprise-grade) if you have sufficient bays and connectors. That's a very cheap incremental upgrade path.