This isn't a complete answer, as I admit I don't know the complete answer, but can't fit into a comment.
Short detour - regarding SQLOS memory there is a wealth of information coming from a guy that worked on the internals of SQL Server storage team - Slava Oks. He has lots of articles on MSDN blogs regarding the SQLOS memory manager and they are all worth a read. Now I know we're on to SQL Server 2012, but the info is valuable nonetheless.
Now, regarding your first question, if there's a limit of max memory taken by db page cache before being cleared out and how is it controlled, I'll quote his word on it.
From article SQLOS's memory manager and SQL Server's Buffer Pool:
Buffer Pool commits pages on demand. Depending on internal memory requirements and external memory state, it calculates its target, amount of memory it thinks it should commit before it can get into memory pressure. To keep system out of paging target is constantly recalculated. Target memory can't exceed max memory that represents max server memory settings. Even if you set min server memory equal to max server memory Buffer Pool will only commit its memory on demand. You can observe this behavior by monitoring corresponding profiler event.
From this article's comment I understand that SQL Server uses a LRU algorithm (LRU = least recently used). If you really need to go in depth, SQL Server's LRU algorithm in particular is described in the following research paper: The LRU-K Page Replacement Algorithm For Database Disk Buffering.
Now, for your second question, the log caches are not really exposed so they can't be changed/tuned, as they are a part of the SQLOS internal memory structure. Quoting from an answer from MSDN forum:
Essentially each database has a log buffer/cache for its transaction
log which is a small contiguous memory allocation, that is 60K in size
and used by active transactions, and flushed when a transaction
commits, or when the buffer space fills up. Multiple active
transactions can be interleaved in the log buffer, and if any one
transaction commits, the buffer memory is written to the transaction
log file by the log writer. If the space fills up, the contents get
flushed to disk allowing the buffer/cache memory to be reused. This
is why log IO can range for 512bytes to 64K (its actually 60K), but it
is always sequential so varying write sizes doesn't matter that much.
The format of the log records is different than data pages as
documented in the BOL
(http://msdn.microsoft.com/en-us/library/ms190925.aspx), so the size
of a log record is variable, but the size of the log buffer/cache is
consistent.
You can't control plan cache size manually. The following Connect item describes both the fact that they won't be adding a knob any time soon and also that Resource Governor might be marginally useful in a few narrow use cases:
http://connect.microsoft.com/SQLServer/feedback/details/293188/amount-of-ram-for-procedure-cache-should-be-configurable
However, as I've alluded to in the comments, there are other ways you can make the plan cache more effective (e.g. use the "optimize for ad hoc workloads" setting). Kimberly explains this in greater detail, but essentially, this setting places much smaller stubs in the cache until the same plan is used more than once, and only then does it cache the whole thing. Under the default configuration, and especially in cases where a lot of dynamically assembled SQL is in place, single-use plans often waste a lot of space in the cache. If you reduce the amount of wasted space these occupy, you leave more room for plans that are used more than once, and those are precisely the ones you want to keep around anyway.
Best Answer
Here are queries that will give you buffer breakdown and plan cache breakdown per database. Note that plan cache is broken down by MB, not by pages - I don't know of a handy way, off the top of my head, to calculate the pages used by the plan cache (you'd think it's simple division, but not necessarily).
On my test instance there are cases where plan cache is larger than the buffer pool for a given database.
The buffer pool contains both the data cache and the plan cache. But AFAIK sys.dm_os_buffer_descriptors only contains information about the data cache (index and data pages), so it does not necessarily reflect the entire buffer pool. The cases I saw above seem to support that theory.