Questions bad block and reallocated sectors count

Yes it seems implemented technology is named “Offline Defect Scanning and Sparing” and SMART is for reporting. It was adopted as early as year 1995.
Maybe ask WD directly which standards they use.

i not found informations for “Offline Defect Scanning and Sparing” and year inplementation

You will not find it online. Each manufacturer implemented differently as there seems to be no universal standard. Most likely it was implemented similary to SCSI drives Predictive Failure Analysis (PFA) specification “x3t10/94-190”.

To know if drive support defect recovery you have to check exact model specification for example:
https://documents.westerndigital.com/content/dam/doc-library/en_us/assets/public/western-digital/product/data-center-drives/ultrastar-sas-series/product-manual-ultrastar-c7k1000.pdf

If this technology of automatically reallocate bad sectors does not have a standard and a name, then how do you know that it really exists?

I know because this function report it to SMART as reallocated sectors. Which is not standardized(or standard is not public) is how it is implemented for each manufacturer. But you have a valid question to ask to all major companies how they implement this and if there is industry standard.
It is theoretically somewhat easy to reverse engineer(which is against WD “terms of use”) how it works in each firmware so it possible to know that it does exist just it won’t have name as variable and function names are lost when firmware is compiled to machine code. If they don’t tell how this works then it only encourages to use reverse engineering this is not something which has to be secret to customers whose data is at risk. Try to search the drive specification I published using keywords “spare” or “defect” and you will see that function is implemented.

Is having SMART technology indicative of having automatic technology for realocating defective sectors?

SMART is just a report?

Yes as otherwise there would be no reallocated sectors to be reported. Can you be more specific for which drive you have?

To answer your questions:

If I have an HD with some badblocks and Reallocated Sectors Count and I download files from the internet will these files be recorded in these defective sectors and will they be corrupted?

No, it won’t use those remapped sectors and pending sectors will be remapped on write operation to spare sector.

If I have an HD with some badblocks and Reallocated Sectors Count and I burn a DVD disc of files that are on that HD will these files be corrupted in the recording creating a DVD of corrupted files?

No only if you have uncorrected sectors. But if you have run out of spare sectors and have run Windows chkdsk to mark bad sectors then those sectors are zero filled and some data lost.

Does HDD and operating system have any automatic function to allocate and separate defective sectors from the HDD and prevent these sectors from being used?

HDD has spare sectors to allocate but OS has only option to mark unreadable sectors as bad if HDD controller fails to recover those.

the files are saved in bad sectors of my HDD? not automatic reallocated separated sectors?

No files are saved only on good sectors.

If I burned DVD discs from files that were on this HDD then will I have to discard the discs because they are corrupted? If HDD has bad block, sectors, defective reallocated sectors count then this dvd disc is corrupted?

No

If an HDD has bad blocks and bad sectors, will the files I download be saved in these bad sectors?

No

In my research on HDDs I found only information about SMART but SMART technology does not reallocate and automatically isolates defective sectors SMART is only a report

That seems to be true, keep researching.

do you have the name of this technology present in the hdd firmware?

the isolation and reallocated of the defective sectors of the HDD is done by firmware of HDD or SMART technology?

All is done in firmware and SMART is only for reporting. I sent you a PM message for other forum were you could ask this question.

the answer to my question is just firmware and not SMART?

this forum that you posted is the best forum for doubts hdd?