You have many questions in a single post.
So in your order:
1) I want to buy a .com domain name that is [supposed to be] expired for 64 days now (according to whois.net)
Never use third party whois servers, query directly the registry whois server, so
whois.verisign-grs.com in your case. It will display various dates as well as status values, which are all relevant to your case. This output would have helped to help you troubleshoot your case.
In the meantime have a look at https://www.icann.org/resources/pages/gtld-lifecycle-2012-02-25-en that displays the typical life cycle of a gTLD domain name.
2) DNS say the domain does not exist.
The DNS does not give you this information because a domain name can be registered but not published in the DNS for various reasons.
whois is the appropriate public interface for this question. A warning though: a domain not seen from a whois query, hence not registered is not necessarily always available to register as some are reserved by the registries or not allowed to register at all, and this many not always be seen through whois.
3) Wayback machine shows it was a parking 3 years ago but since then it's down.
This does not help in any way, a domain name can be registered without having an associated website, for example it can be used only for emails
4) Icann Whois doesn't know about this domain.
Which will always be the case as ICANN whois server, or more precisely IANA ones will only have data about the TLDs.
5) Whois.net and gandi says it was registered by [censored] and it is expired for 64 days but still in redemption period.
If it is in redemption period it means it has been deleted, but will be kept like that for some time, typically 30 days, before being really deleted.
6) Other registrars say I can't buy it because it's registered.
That is logical, they could just transfer it to you if it was not already in a deletion process (and if you had the current owner approval of course)
7) I didn't see the domain on any auction site.
They are no exhaustive list of those, and there could be private negotiations anyway.
8) Legally speaking if the domain is really expired who is the "owner" of this domain ? Icann ? old registrar ?
First, we all use "owner" for a domain name, but "registrant" may be more correct. Because you never own a domain name, you lease it for a specific time, like a phone subscription. Your contract with your registrar is from the domain creation date up to the expiration date. After this date you have not paid (or not yet) for the domain name to continue existing. Through some complicated process (auto-renewal) it may get extended and the registrar might keep it around for some times (typically up to 45 days) but as long as you do not pay the domain is not really yours anymore.
This would be an interesting question for a lawyer, and I am not one. What is sure is that the domain name does not become ICANN property nor the registrar property. There are various regulations about that.
Let us say something like: it is protected during that time so that no one can have it and its past owner has a preventive priority to keep it by renewing it.
9) Could a registrar confiscate a name forever ? (for no fee ?)
No it can not. They were various loopholes in the past but now the various methods are fixed and registrars are very constrained.
See their agreement with ICANN at https://www.icann.org/resources/pages/approved-with-specs-2013-09-17-en#raa and the "Expired Domain Deletion Policy" at https://www.icann.org/resources/pages/registars/accreditation/eddp-en
You can read in it:
126.96.36.199 Where Registrar chooses, under extenuating circumstances, to renew a domain name without the explicit consent of the registrant, the registrar must maintain a record of the extenuating circumstances associated with renewing that specific domain name for inspection by ICANN consistent with clauses 3.4.2 and 3.4.3 of this registrar accreditation agreement.
The "Expired Registration Recovery Policy" at https://www.icann.org/resources/pages/errp-2013-02-28-en may also be of interest to you.
10) Can I trust [censored] to behave ethically ?
How do you suppose anyone there could answer this question without having the name concerned? And even with the name of the company, the answers would be mostly opinion-based and not fact-based so kind of off-topic for here.
11) Will they charge the 70$ if error is on their side ? (no whois update) How great are chances to see the domain land on auction site if I contact them directly ?
Impossible to answer. When a domain name expire it could be put under auctions or specifically offered to some parties that have put a "back order" option on it. Various registrars offer this with option, often with part of the prices given back to you in case the domain name does not finally land in your hand.
12) What should I do ?
This is probably the only actionable item in all your questions, but you will probably not like the answer, even if it is the most reasonable way to solve this problem.
However, here is the naked truth: specially now with all the new gTLDs, there are so many choices that it is silly to devote too much time on a specific domain name.
If you see one already registered and besides a quick contact try with the current owner, if you get no reply or discussions starting on price, you would be much more advised to make your brain work and find another domain as good as this one, but being free, and just register it.
This will save you a lot of money, time and energy. Even if you think, either as an individual or a company, that your life or business plan completely depends on only this very specific domain name that is not available, you are mistaken. Companies in the past have spent millions of local currencies to get some domain names they found attractive... to sometimes just abandon it 2 years after or even failing to really use it in any way. As for individuals you may want a specific name for vanity reasons (like it is your family name or something like that), but you will learn that your vanity could express itself just as well through another name and/or TLD.
The only case where you can not change the domain name is when you already think about reselling it later on because you associate some specific value to it.
14) Complain to icann about missing/lying whois information ? => does this operation gives me special rights ? I don't want the whois to be corrected for someone else registering it before me
There is a specific form at ICANN to use when you want to report problems in Whois output (but I do not think that you are in this case anyway), like missing or obviously fake data.
It is at https://forms.icann.org/en/resources/compliance/complaints/whois/inaccuracy-form
The procedure is as follows: ICANN will contact registrar if your complaint is accepted, the registrar will need to make sure the data is fixed in some time frame, and if nothing happens the domain may get suspended or deleted. This would not give anyone specific privileged treatment, if the domain name becomes available again it will be under the "first come first served" way of doing things.
15) If not what type of dispute could I open at Icann ?
You did not provide enough information to diagnose your case.
But, if you had legitimate interest on the domain name, like a trademark, you could use the specific UDRP path. Note that it takes some time and money (but less than going to court), and you need specific advises from legal counsels that are specialized in this. Again, for a domain name that is about to be deleted it is not a good idea.
16) Should I try to get help from another registrar ?
Why do you think another registrar, with ultra low margins on selling a domain name, would specifically want to help you?
The only thing they can do is start a transfer and for that you will need the agreement of the current owner of the domain name, which does not seem to be the case in which you are.
17) Any special advice ?
This answer to point 12 and when you post here if you want real useful answers, please give more factual details and less rants.
18) EDIT: Finally the domain name was bought by some major [cybersquatting] company that offers to sell it back to me for 2000$.
You would have avoided yourself a lot of lost time and energy if you just did follow the advice on point 12.