Google tries to use different data to determine if a site is spammy or not...I feel domain age is one of these data points to help it determine rank. I have an SEO background so Ill try to answer each of these.
- How is this with parked domains? Do they also get positively recognized by search engines even when parked? Or do the domain needs to be developed for this?
I have never seen a parked page come up in search results. But if you search for a name in quotes you can see what is ranked.
for example
southamericaproperties.com
https://www.google.com/search?q="http://southamericaproperties.com"&oq="http://southamericaproperties.com"&aqs=chrome..69i57.7312j0j7&sourceid=chrome&ie=UTF-8#q="southamericaproperties.com"
you can see there is no description associated with the parked name so very unlikely to match any keywords to that name. So to answer your question yes for Google rank you would need to develop the name with all the seo elements in place such as title and meta tags and content on pages.
- How is this with domains that have no content at all (neither developed nor parked)?
see above reply
- Is it better to build an own "For sale" page instead of parking a domain to build trust?
the more content associated with a name the better but not sure how much content on a for sale page
- Does it make any difference when I use robots "noindex" or "index" in my html when using my own "For sale" page?
no index will exclude all bots from crawling your domain. you mention in your meta html tags. Robot exclusion is done on the robots.txt file. all sites have one in the above example its located here...
http://southamericaproperties.com/robots.txt
this is the one for namepros
https://www.namepros.com/robots.txt
they actually have some really funny comments in there
- Or is all above wrong and does it have rather to do something with possible backlinks the domain accumulated over the years?
little debate over this but I will say my opinion is backlinks certainly do matter. both the total number and more importantly the power of the links pointing back. (is it 1,000 links from dead blogs and free directories or 1,000 links from CNN and Forbes big difference)
So not sure if this answered your question but if your looking for SEO value of a domain then.
1. yes age has some role in the Google ranking factor older names tend to be trusted more over newer names
2. yes back links do have value that help boost the names authority in the engines even if they are "nofollow" links they will provide traffic to the domain.
3. yes a fully developed domain with lots of original content will perform better in search than a parked page with no content or SEO elements.
4. you should NOT exclude good robots (ie google and bing) from your domain but you may want to exclude the spam bots that inflate your domain hits like ones that gather information. This should be done on the robots.txt file
So as you may guess a previously developed site that had content and was ranked and is older will provide more traffic assuming you develop the name compared to a brand new hand reg that was just purchased today. Unless you have one word names like beer.com or mistype names looking at age, backlinks and alexa rank can give you a good idea of the amount of traffic you may get from an expired domain.
None of this of course takes into account the name itself.
As a domain investor I personally would rather have blockchain.com with little traffic and age vs and hypothetical aged blockchainalertsinthenews.net with a lot of back links....
An SEO developer may choose the 2nd name. I guess you need to ask yourself. Are you investing to build out and develop or investing to sell names?