Syslog Explained

Question # 1:

By default, switches send the output from system messages and debug privileged EXEC commands to a logging process. The logging process controls the distribution of logging messages to various destinations, such as the logging buffer, terminal lines, or a UNIX syslog server.

http://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst2950/software/release/12-1_9_ea1/configuration/guide/scg/swlog.html

Questions # 2, 3 & 5:

The logging levels are configured in terms of their precedence based on the table shown below:

So for Question# 2, based on options the precedence holds for:
emergencies, alerts, critical.

for Question # 3, based on the options the precedence holds for:

emregencies, alerts, errors, warnings

for Question # 5, based on the options the precedence holds for:

emergency, critical, errors.

For more info, please check below link:

http://www.cisco.com/c/en/us/td/docs/wireless/access_point/12-3_7_JA/configuration/guide/i1237sc/s37sml.html

Question # 6:

A syslog server separates messages according to their facility type. This command states the facility to which messages generated by the router belong. 

Valid facilities are  auth,  cron,  daemon, kern, lpr, mail, news,syslog, local0 through local7, sys9 through sys14, user, and uucp.

http://www.cisco.com/en/US/products/sw/iosswrel/ps5207/products_command_reference_chapter09186a00801a8086.html#wp1100231

http://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst3560/software/release/12-2_52_se/configuration/guide/3560scg/swlog.html#wp1035270

Question # 7

To configure the system to apply a time stamp to debugging messages or system logging messages, use the service timestamps command in global configuration mode. To disable this service, use the no form of this command.

service timestamps [debug | log] [uptime | datetime [msec]] [localtime] [show-timezone] [year]

no service timestamps [debug | log]

http://www.cisco.com/c/en/us/td/docs/ios/fundamentals/command/reference/cf_book/cf_r1.html#wp1030116