The approach you take is a function of your victory condition (VC). The higher the difficulty of the game, the more focused your VC must be. In addition, if you are moving up to a new difficulty it is more important to focus on one VC. Once you have a handle on Monarchy you'll probably find you can waffle for a long time before 'deciding' how you are going to humiliate the AI.
The reason I bring this up is because Domination and Diplomatic are not 100% complimentary. I'm not saying you can't aim for both, but it is more difficult if you try. For simplicity, I would say pick one and aim for that.
It also depends on why you are playing - if you are trying to score high or with an impressive early finish you will take a different path than if you just want to cruise the game.
For example:
-i have to be better at trading ! (bad trades+no trades early on hurt me )
If you are going for domination it may be a good idea to restrict trading - you don't want the AI to advance fast so that your horsemen and swords are facing pikes and muskets by the time you are ready to attack.
If you are going for an early/quick diplo then you want to trade not only to increase your commerce (and research ability) but to make sure the AI keeps pace so they can give some assistance with a new tech every so often to trade.
-i should space out from my core cities to a CxxC spacing i believe, i just get caught up in grabbing more land space with a CxxxC spacing. and then not filling in.
Here I might get into a little trouble - I'd listen to vmxa for the best results. I tend to space my core a little wide if I am going for space or diplo - I also space wider at the easier difficulties. Tighter spacing for conquests/domination is common.
-is it safe to assume i should stick with a path of either building banks/and sliding the research bar to 0% and buy my techs/trade? or libs/unv and 100% research?
Although there are some min/max gambits in higher level games, I think this is fairly sound advice. Markets are always good for the luxury multiplier regardless of which path you take. Part of the decision will be based on your VC.
If you VC is domination, then you may want a slow tech pace and you'll bank the money to rush/upgrade units. You will 'tech' by pointy-stick - or the Great Library build/capture. And aim for an early finish. On the other hand, you may want to out tech your opponents so you have more powerful units, in which case libraries/universities could help. This likely won't be an early finish, however.
If your VC is space/diplomatic then you'll want to go libraries/universities for fast finish and you'll be researching the entire game.
Of course you could go for the Great Library - in this case you want to maximize income and plan your library/university builds for just prior to its expiration (assuming you plan to continue researching).
The key here is making sure you are getting your worth out of the building. If you are at 100% science for long periods, then the bank is costing you 1gpt (per bank) and you are receiving nothing for it. Likewise, if you are at 0% science for long periods then the libraries and universities are doing nothing but costing maintenance. The danger is that you build both and you sit at 50-70% research. You may get the use out of each building but you are 1) paying maintenance on all of them and 2) at higher levels, 50-70% research may/will not get you to techs first and won't give you enough money to make up for the loss of a monopoly tech.
As I noted, the exception is if I am already researching at 4 turns per tech and still have access capacity on the slider - then I build banks. I'll build more of them if I have Smiths because then there is no gpt cost. However, you then need to decide if the shields used to make the banks would not be better used as units. The answer to that may/will be different for domination than with diplo.
I also got to republic first so i am going to switch to republic instead of monarchy.
Without resurrecting the old monarchy vs republic debate, I think you'll find this to be a good choice. Also, in the game you previously posted I believe you were a republic? So did you go through anarchy twice? Once to go to Monarchy and then to Republic? If so, I would suggest you not do this. This is part of knowing your VC. Decide which government you will need and make one swap.
no more ROP's and trading 2 lux's and i am not going to supply Korea all this time !! lol
I fully agree - no more ROPs, at least until the turn before the UN vote.
Regarding luxury trades - these are okay if you are doing them from a position of strength or mutual (by which I mean you are getting the better deal) trades. I think you will find that, after you are comfortable with Monarchy, you will be gifting luxuries to the AI to help them keep up with tech research. But for now, make sure you are getting a good deal and not feeding the beast!