First of all I have to say that I have been playing all my CIV 5 games the last 3 months in the GEM mod.
Part of that is they adress a couple of the issues you have brought forward.
I agree with the first point, the 2nd one, the 3rd one to an extent, and the 4th.
Ways to implement this, that imho still remain elegant are:
1). Show iron deposits when researching mining. One of the reasons why swords are so incredibly underwhelming is that you need to invest heavily, while taking a huge gambit.
If you know you have iron deposits nearby, you can plan ahead and invest in the very expensive ironworking tech. Also slightly increasing the strength of the swordsman by 1-2 points will help out, OR give the swordsmen bonus to attack cities like they had in Civ4.
2). This one is noticably tougher to solve. Part of what irritates me is that the lancer is a unit that counters itself, and not only that but it is countered by its previously unupgraded counterpart (the pikemen).
The best way to implement this would be introducing a new melee unit around the same tier. Historically there were multiple improvements to the 'pikemen' to deal with mounted soldiers up to cavalry. I even suggest completely removing the lancer all together and substituting it with this new unit.
3). Liberty is a tricky thing to touch, and it power is directly linked to the amount of happyness you can muster early, versus the amount of research boost you get from Tradition + NC.
I personally never believe in one strategy beats all line of thinking, and I have had games where I went a liberty opening and still had a T80 NC with a total of 6 cities.
Maybe the tree needs a little tweaking, but not to much.
4). The honor tree needs some tweaks. I have been advocating for a while now that the "X free units" policy in the former Freedom tree should be put into the Honor tree, and I think this is the perfect moment to do so.
It always has been an incredibly underwhelming policy for just that benefit alone, and its would be a great fit to merge it into one of the already existing policies.
Also I think the opener should just give culture for all military kills you make, not just barbarians.
Certainly this would be the same as monty's UA, but the number can always be changed, it would still stack with monty's UA, or monty's UA could simply change. Monty is already always a pushover in all my games anyways, so a little buff won't be pushing it.
For the rest of the changes I personally would want to see
I think they should finally allow you to 'rushbuy' items for the equivalent cost of the
remaining hammers. This always has been the case in all the civ games, and it actually makes sense both gameplay wise and 'reality' wise.
If I invest 5 turns in building something, and I want to rushbuy the remaining 5 turns with gold, I should not be paying the full amount still.
The Piety tree should also be slightly revamped. The finisher especially is incredibly underwhelming. Not only because the effect is relatively weak, but mostly because it lost a ton of its value when you will be able to attain it. Also settling GP's, something seriously has to gone awry in your religion game if you have to resort to settling your Great prophets.
Also some of the pantheons and beliefs need to be tweaked. Some are just much better than others, and some don't make any sense.
F.e. why does Tithe count for all cities, foreign and domestic, while its culture counterpart only counts for foreign cities.
Monasteries should not be a believe, but should just be a building everyone can build. It gives a very underwhelming effect, that becomes good if you got two very specific resources in your vicinity.
Also the musketmen tech is very awkwardly placed. Every single unit in the game has its upgraded counterpart a good amount of techs spaced between them, but Longswordsmen -> Musket are right next to eachother.
Redo the American UA, its useless, anyone who says otherwise is fooling itself.
I probably got another 10 points, but these are the immediate and most prominent balance changes I can think off.