1) If you use vi-logger in the vMA it doesn't depend on syslog setup in ESXi. If you configure the syslog settings for ESXi it can be any syslog server. I've used it with Splunk and others have mention other tools that work just fine.
2) It's pretty straight forward to setup syslog - just configure the remote host and port. The settings take affect right away. If you're using vi-logger you just have to use 2 commands. I have more details in this book . Here's a sample setup
[vi-admin@vma41 ~]$ vifp addserver esx01.mishchenko.net --authpolicy fpauth --username root
root@esx01.mishchenko.net's password:
[vi-admin@vma41 ~]$ vilogger enable --server esx01.mishchenko.net
Target Server: esx01.mishchenko.net
hostd ... Enabled
messages ... Enabled
vpxa ... Enabled
[vi-admin@vma41 ~]$
The default location for log files will be in /var/log/vmware/ and vi-logger will maintain a folder for each host.
3) If you're configuring syslog then just add the remote host and port. No need to restart anything.
As an aside, ESXi maintains its log files in UTC. It also sends everything that is logged in /var/log/messages to the syslog reciever. You can't at this point configure what level of data ESXi sends to the syslog recever.