Cache Warming and Cache Collection is always performed whenever a database is started independent of how long the server has been running, except for these conditions:

• cache warming is not done when it is explicitly turned off by -cr-
• cache collection is not done when it is explicitly turned off by -cc-
• neither warming nor collection is done when the database is participating in mirroring/HA or is started as read-only or the database was started for the purpose of upgrading or dropping it
• cache warming is also not done in the case that the database needs to go through recovery when it is started.

I think your last question is asking if the cache warming process would cause existing database pages (from previously loaded/running databases on the server) that were already in the cache to be replaced? If this is the question then the answer is no. Cache warming will automatically stop if there are no free cache pages.

Also note that cache warming will be stop if there is a significant amount of other IO (i.e. IO not associated with warming) occurring on the server. Therefore if a database is loaded on a server that has other database activity and that activity is requiring IO then it is likely that the newly loaded database will not be "completely" warmed (where "completely" means warmed to the same amount that it would be if the database was loaded on a newly started server).

HTH