Next project - toilet in main bathroom ... :-(

It is a dual flush and has a concealed cistern and very little/no
access. Was bought from MFI just before they went under, so couldn't
find any documentation about it. I am also happy to admit that I have no
clue how they work...
The toilet itself is siliconed to both the wooden panel (will be
difficult to remove without damaging the panel) and the floor.
See photos here (with the panel slightly removed, but can be fully
removed by undoing the flusher button):

http://tinypic.com/r/qpm25f/8
http://tinypic.com/r/av42b/8
http://tinypic.com/r/25s7k7k/8

Problems are as follows:

- For the last few years it would not flush as it should - the only way
to achieve a full flush was to press AND HOLD the flusher button until
the cistern was empty. Any other way would only provide a half flush.
Sounds silly, but we just got used to it...

- A couple of weeks ago a new problem was introduced were the cistern
started to fill up very very slowly - takes around 15 minutes to fill
up, and a bit of an issue with 4 people in the house... Also, the
flusher button seem to occasionally get stuck in the pressed position
with water flowing straight into the toilet until released (quick press
on it and it returns to the correct position).

As you can see from the photos, access is very restricted. The worktop
is L-shaped, approx 2.5m x 2.5m with a sink siliconed to it. It is also
siliconed to the wall/tiles.

Not sure if relevant or not, but we are in a very soft water area -
still using the same electric kettle after 7 years and it looks as good
as new inside.

Any tips as to where to start investigating for the source(s) of the
problem(s)?

Many thanks in advance.