Can't help with the grouting but I've worked on lots of building sites and nicked lots of the sealant they use and its always the same one which can't be a coincidence
They all use Dow corning 785 sealant so its all I use as well
scrape out as much of the old sealant as you can, you'll never get it all out though.
Before you put the new sealant on rub down all around the area with a lint free cloth and methylated spirits.
If your steady with the sealant gun put a small bead around the area, most people put it on much to thickly and you end up in a right mess as when you try to smooth it out the excess goes everywhere
When smoothing it down you should be looking to just flatten it into the gap with barely any pressure or excess sealant building up on your finger as you go along, it really helps if you dip your finger in a weak solution of washing up liquid as your finger will just slide over the top leaving a lovely smooth bead
If your not steady with the sealant gun or just know your going to mess it up
a foolproof way is to use masking tape, tape out the width of your joint top and bottom, put your bead of sealant in, smooth it down as above, then remove masking tape straight away and leave to dry for 24 hours