1) Turn off AUTO SHRINK. Its evil and can be source of long term performance issues as it can lead to file level fragmentation.
2) As mentioned above, it looks like AUTO CLOSE is turned ON. You need to turn it off as this is another one that is detrimental to good performance. Why? Every time the last connection is closed, SQL Server is trying to shut itself down and this leads to clearing the procedure and data cache. These two are the ones that support the good performance by reducing the need to fetch the data from disk, which is very expensive compared to reading from memory. And generating execution plans is a cpu intensive process and your sql server has to generate the plans after coming back from auto close. Now taht you know what its doing, go ahead and turn off AUTO CLOSE.
3) SQL Server is NOT really doing a DBCC CHECKDB but displaying a message after reading the boot file where it stores the last clean ran DBCC CHECKDB date. Its simply writing to the log file and not really running the CHECKDB here. It looks like it has been more than 2 months that you ran CHECKDB and its a good practise to run the CHECKDB in regular intervals as you can.