Access to logs of startup and shut down

I'm not sure if I correctly undrestand your question, however to address what you asked (Bold section), you should change logrotate configurations.

Have a look at this file:

less /etc/logrotate.conf

there should be lines like:

/var/log/wtmp {
    missingok
    monthly
    create 0664 root utmp
    rotate 1
}

If you remove these lines from file, "logrotate" does not remove this log anymore, you can change "monthly" to "yearly" to make it remove files after a year; rotate 1 means keep one backup before removing the old one which comes to:

$ ls /var/log/wtmp*
/var/log/wtmp  /var/log/wtmp.1

If you change it to 2, you're going to get:

$ ls /var/log/wtmp*
/var/log/wtmp  /var/log/wtmp.1  /var/log/wtmp.2