Ill try to shed some light on a couple of your questions.
1 - Dose/Tamp takes a bit of practice. If possible, get some cheap roasted beans that you are not particularly interested in drinking and try different combinations of grind and tamp pressure. Many people do not tamp hard enough. Most figures on the web suggest 30KG of pressure. If you have bathroom scales, see if you can use them to give yourself an idea of how hard 30KGs is. When I am dialing in a new bean on the grinder, I set up a shot glass (30ML) on one spout and a small cup on the other and keep grinding/tamping until I get the 25-30 second shot. Invariably, if I have the grind and tamp right (and have not overfilled the basket) the puck is pretty dry.
When I dose the basket (I have a rocky with doser), I slightly overfill the basket, tap down on bench to settle it, level off (removing excess) with an icy pole stick and then do my tamp. I have found that I never overdose my basket these days. This helps with a dry puck. It also seems to stop any leaking during the shot.
As for leaving the machine on for extended periods, I would say no. Im sure you will find a lot of articles on the web talking about temperature stability or instability of the Silvia. I find that my shots are definitely better when the machine has had 10-30 minutes warmup (with empty basket/portafilter in place), but if you leave it on for too long, the water in the boiler gets heated up multiple times and will not taste as good in my opinion. It can also get too hot for making good shots.
2 - I dont think removing the water tank is an issue. The only reason not to take it out is the hoses will spill water if not careful. I dont take mine out that often, but it should certainly be taken out and washed every now and then because even with filtered water going into it, some yuck develops.
3 - Hmm. When I do my preheat, water flows through spouts and into drip tray. Is water coming out from places other than the coffee spouts of the portafilter? If so, you might have coffee grounds around the group head - needs a clean. If it is clean, there might be an actual problem. Keep an eye on this. I have my combo also on the stand and never get splashes onto the grinder.
As for the water coming out, if you are not overfilling the tank (keeping in mind the cutout is slightly lower than the rest of the tank) you have an issue. Someone else on this site reported something similar a while ago, Ill see if I can find the post. I know about the overfilling where the cutout is, because thats what I did on day one (and two).
EDIT - Found the thread - http://coffeesnobs.com.au/YaBB.pl?num=1099296647
Answer about leaking is on page 2, but the whole thread might be a good read for you. It deals with a couple of new Silvia owners problems. The drip tray was 4mm undersized on his machine which was causing the issue.
4 - Espresso cleaner is not the same as descaler. You dont really want to put espresso cleaner through your machines internals. Generally, espresso cleaner is a harsh chemical mix. Descaler can be as well, but many people here extoll the virtues of citric acid for descaling.
PPS - The switching on for 3, off for 5, etc. is sometimes called pre-infusion and I dont really know much about it, but it sounds a bit too much for this level of machine.
Hope that helps.