First off, the domain needs to be somewhat relevant to the topic of the site you are redirecting it to.
Second, make sure you actually reproduce the site to allow Google to understand the domain is online and active again before you simply redirect it.
Basically, to do the "expired domain" tactic right, you are going to need to find one with backlinks worth leveraging, on a topic closely related to yours, and put the site back online for at least 90 days before you redirect.
If you're going to do this (and want to do it right) make sure the juice is worth the squeeze.
If yes, then the "age" of the domain shouldn't matter as much as the age of the backlinks.
So if the old links are still pointing to it, the newer domain age shouldn't matter - you should be good. I would use a pages report in a backlink analysis tool (I prefer Majestic, but I know there are others :)) and then pull up the Wayback Machine to see what kind of data it has on the domain. Then work on rebuilding the essential pages from there.
Also, do I need to make the content of the homepage similar to the old homepage?
If yes? When should I replace the content of homepage like after 6 months 5 months ?
1 - yes. 2 - yes, as much as possible. 3 - 3 months minimum. anything after that is great but not necessary IMO.