Yes, mechanical differences are trivial because mechanics are trivial. (for me) What I want is a strenghtened or renewed feeling.
They aren't, however, trivial when it comes to playing the game. And you only get that 'Civ' feeling if you're having fun playing the game. And you only have fun playing the game if you're using strategies that work at least well enough to give you a varied and interesting gaming experience. Which comes back to the mechanics.
I'm not doing this distinction.
Which is precisely my point...
Indeed, if there are player issues as you say so poetically, it is that the game is not accessible enough.
So, if someone finds chess difficult, it should be made easier to be more accessible to people at lower skill levels? Not only is that a rather poor way of looking at things, it seems to defeat the point - a lot of the enjoyment comes from a sense of being challenged in one way or another. You might find an easier game (and as many Civ veterans will be quick to point out, Civ V is not the most difficult instalment of the series to master) more 'accessible' but you'd probably get bored of it very quickly. People who want games that make everything easy for them and who don't mind repetitively doing the same unchallenging things over and over play games like World of Warcraft, not Civilization.
Sometimes it just appears that expansion will be impossible because you simply run out of happiness, with the same ressources you already have around, everything built and of course no money to bribe CSs.
That simply suggests the need for a different strategy. No money to bribe CSes? Look at what you've built - do you need it all or is that maintenance unnecessary? Do you have trading posts everywhere you need them, and are your cities working them? Is there anything you can sell to an AI to get money? You very often have duplicates of at least one resource (the game is specifically designed to cluster resources for that purpose) - very often you can trade these for different resources another Civ has (although that becomes harder later in the game as a general rule, as other Civs have expanded to get their own sources of these resources, or have more AI trading partners to obtain them from). Settle near the bonus/luxury resources that let you build happiness buildings - horses, ivory or stone.
Or if you want to expand quickly and don't have sufficient resource access, try focusing on Culture production; that way you can reach the social policies you need to promote happiness more quickly. Good early ones are the Piety one that provides happiness for each religious building (particularly if one of your resources is Dyes or Wine, so you can build Monasteries), and the one (in Honor, I think?) that provides 1 happiness for every garrisoned city.
Of course all that could be OK if at least we would have an insight on the real use of cities, aka how to go to victory, but those are so far away that it's difficult to focus on something else than simply power, power that is usually obtainable in Civ with settlers and grabbing land, but not in this one, as you are constantly harrassed by unhappiness or negative income.
Civ V isn't about cities, it's about population. Population generates science, which drives everything. Population works the land, which produces commerce. More cities are still better in general - they give you extra production slots, let you build duplicate buildings, allow you to gain access to additional resources and territory more effectively. But consider that 4 population in City A produce as much unhappiness as 1 population in City B, at the same time as creating 4x the research and 4x the tile workers or specialists. This is why you have specific policy branches designed around 'small' or 'large' empires - most obviously Tradition (with various bonuses that apply specifically to your capital) vs. Liberty (with extra settlers. workers and boosts for extra cities). You gain more culture more quickly with fewer cities, which can be used to produce happiness-generating policies. You build National Wonders more quickly with fewer cities, but by contrast can't be building as many other things at the same time because you have fewer production centres. The entire game engine is built around that trade-off between the inherent advantages of more, but smaller, cities and the game engine-promoted advantages of fewer, larger cities.
You need to appreciate this before you can decide what your favoured strategies are going to be. And if you still genuinely have trouble expanding past two cities, concentrate on developing a strategy that maximises the population growth of those two cities and managing their happiness, science, culture and gold outputs.