In the spirit of quick answers to quick questions:
1. No sliders in CiV. If you want more science, grow your population, build science buildings and populate scientist slots (and unpopulate them to reprioritize away from science). The closest thing to spending gold on science in CiV is the research agreement. For more gold, assign citizens to work tiles that yield gold and build gold-multiplying building (markets, banks, etc.). You can also sell spare strategic and luxury resources for lump-sum gold or gold-per-turn.
2. Diplomatic penalties are legion, and most last 30-50 turns, although some are permanent. They manifest themselves in AI opinions of you, and can be observed by mouse hovering over the "Friendly, Neutral, Hostile," etc. labels in the diplomatic screen. Big no-nos are denouncing or DOWing civs you have a DOF with and breaking other promises you made (promise not to nearby expand, "just passing though" challenges to units near AI borders, continue spying when you promise not to, etc.) and some for just pursuing your strategy (covet your lands, warmonger penalty if you eliminate a rival ("hey, he started it, and I ended it, by exterminating him. What's the big deal?", etc.). Bunch of threads complaining about how touchy and unreasonable the AI can be (I find diplo generally logical, but I suspect I'm in the minority). On diplo victory, beeline to Globalization, build the UN, and have a stack of gold to ally every CS you can find.
3. Big no-no. Unpopular with pretty much every civ (except maybe the Mongols, whose UA gives them a bonus for doing the same).