Can super user write into read-only files?

It's normal for root to be able to override permissions in this manner.

Another example is root being able to read a file with no read access:

$ echo hello > tst
$ chmod 0 tst
$ ls -l tst
---------- 1 sweh sweh 6 Aug 16 15:46 tst
$ cat tst
cat: tst: Permission denied
$ sudo cat tst
hello

Some systems have the concept of immutable files. eg on FreeBSD:

# ls -l tst
-rw-r--r--  1 sweh  sweh  6 Aug 16 15:50 tst
# chflags simmutable tst
# echo there >> tst
tst: Operation not permitted.

Now even root can't write to the file. But, of course, root can remove the flag:

# chflags nosimmutable tst
# echo there >> tst
# cat tst
hello
there

With FreeBSD you can go a step further and set a kernel flag to prevent root from removing the flag:

# chflags simmutable tst
# sysctl kern.securelevel=1
kern.securelevel: -1 -> 1
# chflags nosimmutable tst
chflags: tst: Operation not permitted

Now no one, not even root can change this file.

(The system needs rebooting to reduce the securelevel).

Yes, this is very normal. root has no limits on read/write (with very little exception), because he is the root.