I did a bit of unaccompanied traveling in the EU when I was your age. (But I've never hitchhiked.)
As EU/Schengen citizens both of you are entitled to travel quite freely in all these countries. Even if there would happen to be some border controls it would not be a problem. Of course, it's wise to bring your passports so that you can easily prove that you are EU nationals should anything occur.
Being 17 is no legal issue. There is no law that can prevent 17 year old EU nationals from traveling around Europe.
Regarding approval letters from your parents, yes, do bring that. As the answers of @BjörnLarsson and @JirkaHanika now show, it may actually be required in at least one of the countries you mention. And in those where it isn't, it would still be something useful to refer to should police, etc. ask you anything. Here's a very much related answer from a few weeks back.
Moving on, you ask:
Our parents know we are wise and traveling without adult supervision
won't be a challenge for us but they're afraid the most is what if
police asks us to show our documents? Can they send us back home if
they find out we're not 18 and make a case in a court that our parents
No, this won't be a problem. As long as you behave well and don't break any laws, you'll be fine. There's absolutely no way police can legally arrest or deport you merely for being 17 year olds from another EU country. In fact, the EU encourages youth to travel and explore the continent through programs such as Interrail and the Youth Networks. However, should the police ask you anything, it would be useful to have the letters I referred to earlier, as well as the contact information and personal details of your parents.
I would also like to ask, if you, the people who are reading this
question, would let your 17 year old son hitchhike in Europe with his
also 17 year old male friend.
If I had a 17 year old son I would probably offer to pay for an Interrail pass and/or flight and/or bus tickets rather than have him hitchhiking. I'm not necessarily telling you not to hitchhike, I'm just saying what I personally would do. And I would probably call him every other day to check how he was doing, and tell him to be careful and use common sense, guard his valuables, etc.
So, again, I'm not necessarily telling you not to hitchhike. However, do think this over carefully. There are risks with hitchhiking. Consider if buses, trains and/or flights may also be options for you. As always, it's better to be safe than sorry.
However, if you do choose to hitchhike:
Since you are nearly (or completely) physically fully grown males, and since there are two of you, you are at a significantly lower risk than, for example, a girl traveling alone. Still, while hitchhiking one should always be careful. Guard your possessions carefully, exercise caution when interacting with strangers etc. Hitchhiking is, in general, more dangerous than other forms of transportation. So be careful and use common sense to stay away from potentially risky situations. And stay together, two people are always safer than one.
Here are some great safety tips for hitchhiking that someone brought to my attention.
I'd advise you to get a cheap phone plan and maintain contact with your parents. A smartphone with Google Translate wouldn't hurt either.
While hitchhiking, I suggest you stay sober the entire time. Underage drinking can not only get you in trouble with the law, it can also rob you of your sound judgement and thus put you in unnecessary dangerous situations. And also, of course, stay away from drivers who appear not to be sober.
Another issue is accomodation. Not all hotels/guesthouses will allow minors staying alone. Again, I refer you to the related answer for details.