The information you quoted above deals with licensing considerations for these helper processes. I assume you are looking for information on functionality. You should familiarize yourself with the Progress documentation for the release you are using. Start with the Database Essentials manual, then move on to Database Administration. Both talk about the functionality of these processes.
1) What is the difference between APW, AIW and BIW and how its work in progress database ?
These are Progress processes you can run against a database that is online in multi-user mode, provided you have an Enterprise RDBMS license.
The before image writer (BIW) ensures that the transaction notes in full BI buffers are written to the BI file on disk in a timely manner so they can be emptied and made available again to write more notes. You can only run one BIW per database. If you are using an Enterprise license you should always run a BIW. If you don't, writes to the BI file are done by the servers and may be a performance bottleneck for your application.
The after image writer (AIW) performs a similar function for the after image notes. It writes the contents of full AI buffers to the current AI extent so the buffers can be re-used. You can only run one AIW per database. If you are using an Enterprise license and after imaging is enabled in your database, you should always run an AIW. If your database contains important data, i.e. data loss would be a cost to your database, you should always have after imaging enabled.
The asynchronous page writer (APW) performs a few different tasks. From the 10.2B Database Administration manual, page 14-11:
APWs are optional and require an Enterprise database license. APWs are highly recommended
because they improve performance in the following ways:
• They ensure that a supply of empty buffers is available so the database engine does not
have to wait for database buffers to be written to disk.
• They reduce the number of buffers that the engine must examine before writing a modified
database buffer to disk. To keep the most active buffers in memory, the engine writes the
least recently used buffers to disk; the engine must search buffers to determine which one
is least recently used.
• They reduce overhead associated with checkpointing
You can run one or more APWs against a database, and you should always have at least one per database. Follow the information in the manuals to determine whether you may need more than one based on performance metrics from promon.
2) How can me check long run transcations ?
On your database server you can run promon against your database:
Go into the R&D menu, then 1 (status), 4 (clients), 3 (active transactions). If there are any long-running transactions you will see them here.
3) How can we check user licence in database ?
There are a few different ways I could interpret this question so I'm not sure what you're asking. Do you want to know which product licenses are installed on the database server? How many users are connected to the database? How many users have been connected historically? Please rephrase your question in more detail.