2. where can I check what my current rep status looks like?
I have a theory about rep: if you have to ask "how do I check my rep", then you probably don't need to worry about your rep. This is because rep is only important with some strategies, and if you're not playing that strategy, then you don't need to keep a clean rep.
First, we have to be clear about one thing: rep and attitude are two different things. Attitude is how much the AI's like you. If they don't like you, they are more likely to declare war on you, etc. Rep is if the AI's will take your credit. If your rep is broken, then they won't accept any thing that's "per-turn" in your payments.
Rep is useful if you're playing the tech broker strategy. I.e. you buy tech A, sell it to another civ for tech B, then sell techs A+B to another civ for tech C, getting 3 for the price of 1, etc...
When playing the tech broker, because the first tech that you buy is usually expensive, and since no body has 5000 gold sitting in the bank all the time, you usually have to play some gold-per-turns in order to get the ball rolling. If you lose your rep, then you can't pay gpt anymore. It makes tech brokering a lot harder.
Now, if you play tech broker all the time, then it is very obvious when you broke your rep: you try to buy a tech, 800 gold + a world map is "close", but after
adding another 10gpt, it becomes impossible!
However, if you're not playing tech broker, then you don't need to pay any gpt to the AI's, then your rep is not very useful anymore.
6. In case I happen to have very aggressive neighbours next to me (e.g. Zulus, Germans etc) what should i do to minimize risk of attack from their side, especially in the expansion period when I really do not want to engage into a prolonged warfare? do trade agreements really help? or should i take a deep breathe and try to conquer as much of their cities as possible, before they take mines? simply put, what should i do to make them smile at me?
Put at least 1 unit in each of your cities that has some kind of resource, preferably 2 in an iron city (note: they don't have to be defensive units).
Put at least 1 unit in each of your border cities.
Put at least 1 unit in each of your cities that can be reached by his units this turn.
Leave some expansion room for them. AIs usually don't attack before they run out of expansion room. This is especially true if you're planning to attack them later. There are going to be some cities that will be too corrupt to help either you or the AI in the war effort. Let the AI found those cities. Those cities will be easy to take later. It will keep the AI in expansion mode longer, meaning less troops for them, and allow you to start your invasion sooner.
Plus what TimBentley said. If you have a choice between buying a tech with gpt from India and from Germany, buy from Germany first.