SQL Server Dynamic Memory management
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.