Please forgive any grammar
I think your grammar is better than many native English speakers'. However, I only forgive poor grammar, not just any old grammar

.
1: Bribes and gifts
used to work for alliance purposes. Now really the only way to get an alliance is to have a military rating that is much higher than the other faction's military rating.
2: It would be nice, but you can't, it is just not an option. You can extort from them, though - if your military rating is higher than theirs, go to the diplomacy screen and ask them for money without offering them anything.
3: Research advanced troop modules and the miniaturization techs. Toward the end of the game, I can usually mount three ATMs on a cargo hull for a total of 3000 (billion) troops. Or mount one ATM on a tiny hull for a vastly cheaper ship. The best way to invade, of course, is by spore, if you are a Super Annihilator race.
4: Influence victory is really just an unfinished military victory. You will probably need to conquer at least some planets in order to spread your influence far enough to win the game, especially in larger galaxy sizes.
5: When the populace is threatening to rebel, build a propaganda center if your are evil. Beefing up the orbital garrison helps a little, as well as building cultural centers on the planet. Building your own influence starbases nearby also helps, and is the only thing you can do to help a mining base. The surest way, of course, is to conquer the other planets around the one in trouble.
6: Both sliders and factories - the sliders represent how much of your potential factory production you are using. If the planet is not building any improvements, all production given by the slider will go to shipbuilding. If you are building improvements and ships at the same time, the ships will build more slowly unless you put all or most of your production (non-research) spending into military production. There are several good discussions of production stretegy on these boards - try using the search at the top of the page for 'factory', 'production', and other related terms.
7: There is
NO rule number seven!
8: On higher difficulty levels, the computer
will get a little ahead of you no matter what. Try not to let it get too far ahead in weapons and miniaturization both, or you will start to have a very hard time of it. You will have to find a good balance between building early warships to keep up your military rating and pouring as much as possible into research to try to keep up with the AI at the same time. It just takes a bit of practice.
I hope that was helpful - bon chance!