Shower repairing grouting and or sealing

The shower cubicle in the attached was installed by the builders in 97. After a while the sealant became stained so 6 years ago I removed it and re-sealed using a generic type. When removing the sealant some of the grout in the corners came out with it so I had the "brilliant" idea of extending the sealant up the wall... see images 727 & 730.

The grouting in the cubicle seems to be OK except at the corners: see 728, 729. The builders seem to have applied the grouting in several layers, see 732.

There is no evidence of any leakage. Until I started reading about tiling and showers on this forum I was feeling fairly confident.

Now I have the following questions:

Materials: are Mapei waterproof fix and grout and Unibond anti mould sealant likely to be suitable? http://www.screwfix.com/p/mapei-waterproof-fix-grout-white-1-5kg/64982 http://www.screwfix.com/p/unibond-anti-mould-sanitary-sealant-ice-white-300ml/95522

Tools: I expect to have to remove a small amount of grout along the corners. Do I need to use any special tools? If so, could somebody recommend a hand tool please? for example? http://www.screwfix.com/p/pro-grout-rake-cutter/17903

Method: Would it be OK to use sealant instead of grout in the corners? if so, should I remove the all the old grout first?

Grout staining: The old grout has become discoloured in some areas to to the growth of mould. I have tried grouting pens, potassium permanganate and bleach. Nothing seems to work for very long. Is there such a grout sealant that works? http://www.tiledoctor.co.uk/groutsealer.html

Do any of these electric grout cleaning brushes work? http://www.amazon.co.uk/Replacement..._sim_79_1?ie=UTF8&refRID=1KKDCTEW0F3KQ9TK7Y6S

Update: when I removed the sealant the back of it was moist at locations all around the tray. Any suggestions as to how this might have happened?

It was possibly due to the fact that the builders grouted in the corner and around the tray. Grout in these areas will always crack after a time and let water in, even when it is sealed with silicon. The best way is to use silicon only.

Update: I found a lot of advice about sealing and grouting on the internet and on this forum. The boss insisted I used grout between the tiles in the corner. According to Mapei's data sheet their waterproof fix and grout is acrylic based so maybe it will have some flexibility.

Having read all the advice on sealants:

I very carefully removed all traces of the old sealant.
I cleaned all surfaces with isopropanol.
I applied the sealant while standing on the shower tray.
I dipped the Vitrex sealant tool in washing up liquid. http://www.screwfix.com/p/vitrex-flexi-tip-sealant-smoother/10994.
After removing the masking tape I smoothed over the edges of the sealant bead.

These steps all seem to be important. The end result looks quite nice. I will wait to see how it performs.