However, does that mean that it is not possible to get the same checksum when write/burn from an img/iso file to a DVD/CD/Thumbdrive?
Personally, I don't bother verifying any install media with checksums. That's because all "media" (including network transmissions) is already internally protected with mechanisms similar to checksum (ECC on disk and CD/DVD drives, and on flash media, CRCs and friends on networks). The main thing that these checksums protect are software defects and main memory errors: the latter are rare, and the former should be non-existing. What I do however do: After burning a CD or writing a memory stick, I put it in a computer, and read it cover to cover (without looking at the content). It's not uncommon to get read errors there.
Having said that: Assuming that the image file is a sensible size (namely a multiple of the sector size of the media), the checksums SHOULD match, if you read only the part of the CD/DVD/Thumbdrive that was actually written. On a burned CD/DVD, the readable area is exactly the size that is written, so there reading the whole media should give the correct checksum without even counting sectors.
I got
Code:
gptboot: backup GPT header checksum mismatch
when the thumbdrive booted
I'm not sure what that message means. The GPT layout has two copies of the partition table, the second one at the end of the media. It could be that the backup copy (at the end of the media) is corrupted or not present. This could happen if the image file is not the correct length (got truncated in transit somehow), but a simple check of the size or checksum should catch that, so this is not the problem. It could also be that the image file was created without a valid backup GPT table at the end, but I would consider that to be a bug.
and my desktop system was unable to connect to the internet after the installation.
But did the installation otherwise proceed as normal? I would think that if the installation works normally, and puts a copy of FreeBSD on your root disk, that the problem with the missing internet connection would not be a problem with the install media, but with some configuration.
Something went sideways during the install due to perhaps my harddisk, having trouble(got S.M.A.R.T. failure from disk utility program), or perhaps it has something to do with the mismatch checksum. So I got new 500G hard disk and will try again.
If you already have a SMART error on the boot disk, it's pretty pointless to proceed. The system you install won't live very long if the disk is admitting that it is nearing the end of its life.
Does this means that I am going to have problems with FreeBSD after installation? Or installing any program for that matter.
If your boot disk is dying or broken, the system is not going to be much fun. I refer to it as "CTD", which is a nasty acronym paramedics use to describe a patient who is "Circling The Drain"; the next stage is FTD = Fixing To Die.
I was going to propose that your first step should be finding a better disk, but you're already doing that.
The second step needs to be finding someone who has tried copying the memory stick install image to a thumbdrive successfully, and have them tell us whether they got that "GPT backup table mismatch" error too. If they didn't, then something is still wrong with the way you write your thumbdrive.