My answers are not authorities and are based on research and other people's testimonies only, while I am at it I'll elaborate slightly more on the subject!
Question on 301 redirection:
1= It may take months and up to a year for all pages from the old site to transfer rank to the new site domain, if what you mean IS THE RANK AND BACKLINKS, of course that's if the old site is well established with good PR / backlink portfolio (yes makes a change from saying profile) and trustrank. I myself would reserve at least one year and leave the 301 redirects there for that long. One drawback is if you take the redirects down, there will be few backlinks that are still pointing to the old domain, and those in time will count for nothing and loose PR juice as what was giving them credibility*** is the old site's redirect, once that is taken down, there is no point of reference as to where from THEY GOT THE OLD BACKLINKS as the old domain has expired, sooner or later will be treated as new links. However, don't let that deter you, as in the meantime, they will gain new backlinks (WHILE THE 301 IS IN PLACE) from new sources and many linkers to the old site and bookmarkers will get the hint after a year's redirect (not all, but at least half of them), so should all even out at the end. that's why the redirect should be in place for as long as possible besides giving time to SEs to index / re-index and recalculate rank etc. I have 301 on some sites for seven years now, why, because some webmasters will never change their links to point the new site (unless you asked them to), for me I tend to hold on to the old domains, so leaving the 301 is no problem.
- 2 = If it's not possible to hold on to the old domain, you have no choice I guess, there is a risk if the old site is an authority site and its domain is bought by a spammer or ends up a black hat site, the risk may be a temporary filter until SEs investigate further to be sure the site is under new management. Let's face it, it was redirecting all links to the new site and all of a sudden becomes a bad neighborhood itself, so it's bound to ring alarm bells and has done for few people who told me so, some had to write to G* for a recon request, though now G* has the "add or remove owners link" on WMT which may help to give them a hint the site is under new ownership, however, I don't think that is its purpose for sure!
Question on Domain Age :
My own judgment is not the domain registration record, but by site age, i.e. when went live / archived, be it on the Internet Archive (or other archiving service) or spidered by a Search engine. Even though one can get the age from the first day of registration from any whoisdomain service, for SEs to count it as live since such and such date, those whois services have to be authoritative on their response and not all whois services can convince G* or other SEs of that fact except bodies approved by legislative means directly. For G*, I think they go by the IA and their own records automatically (if the site is no older than their idex's first inception) and with manual investigation (through various channels other than pointed out here) if it's a very large corporate site, they don't want to upset people of power.
Someone should correct me here if I am wrong, if the domain was never used, it's a new site as far as any SE is concerned!
Site age is about how old is the content, membership, readership and circulation (if news / info site), reputation and backlink profile, brand awareness, new and repeat visitors, innovation, technology etc...
Domain age is about when the domain was first registered, how many owners were involved, and for those years probably the domain was expired few times, if it never went live, IT IS considered NEW once it goes live.
One last thing, when sites change hands let's not forget, if the site (live website) had different owners and each owner re-branded it with their own theme, content and so on, what will count IMO in its current ranking is how close the current content is to the once archived / indexed content, if it's almost exactly the same (titles, descriptions, design, material different but the same subject), that no doubt will boost its authority and rank, but only on those years matching the current current content even if its not the same owner. Note that when URLs and anchor texts are different, any backlinks can be redirected to a hub page explaining that the content has changed and should go to the homepage to choose what to read, at least if the content is on the same theme and subject, a lot of juice will still count and will in time be transferred to the homepage from the hub page and thereafter to where they liked the read and linked to it.
If two years live offering Swiss cheese, then another two years offering essays on Freudian dream analysis, it's best to go live with the site offering one or the other, being greedy and offering the two contents justifying blaming having bad dreams on Swiss cheese, may not be so cheesy even if that holds true in some respects scientifically for all cheeses.
Nice if you inherit the directories, scripts and database which means an identical content under new ownership and that just carries on the site rank with no change, but offering an entirely different content, you might as well say it's a new site, the backlinks sooner or later will be devalued as deemed to be irrelevant, maybe small advantage of visitors regardless of how different the content is for the initial period but will soon fade.
*** they in the same time gain credibility while the redirect is there, hence gain new backlinks anyway!