Yep, there are several underpowered civs that needs a boost, along with Unique Improvements in general. Let me see what could be done in order to remedy it:
Spain
El Escorial: +4 combat bonus against heathens (civs with different religions) and unbelievers (civs with no religion & barbarians)
This way, Spain could have a strong early bonus that fits Philiph thematically, without needing to fund a religion in order to benefit from it.
Mission: +1 food per ajacent plantation and +1 faith per discovered natural wonder
A boost created in order to make missions a bit tad less situational (no need to be placed in a different continent in order for them to become useful) while also rewarding exploration (gotta know where these natural wonders are so they inspire our people!)
Flota de Indias: In addition to its previous effects, you will gain a free settler the first time that one of your units touches the land of another continent.
A way to aid Spain in stablishing those overseas colonies while at the same time rewarding the player for taking a more proactive role at exploration without making them too much to coastatal dependant.
China
Great wall: Can be built over other improvements as if it were a road, can't be built adjacent to more than 2 wall sections, can be built outside your borders as long as it is adjacent to said borders
Not only this would end with "the great wall of spaghetti" (adjacency restriction), but it will also make the great wall way more powerful (only improvement that can be stacked on top of others!) and it will be more of use in the early game when you don't have too much territory yet (it can be built outside your borders).
India
Shagayarta: You can build missionaries and buildings of any faith as long as it is present in your cities without needing to have that city converted to any given faith: just having one follower present will be enough prequisite to build missionaries. All your religious districts have +1 additional slot for buildings (so you may have a mosque and a pagoda on the same city)
With that modification India's religion game will be far more active, allowing the Indian player to tailor the beliefs of its people without waiting for foreign missionaries, all while providing an excellent defense against agressive religious persecution, since religions will be far more resilient inside India's frontiers.
Stepwell: +1 housing if adjacent to a river with sanitation
A small, straightfoward boost to make stepwells viable even with neighbourhoods avaible
Egypt
Sphinx: +1 production if placed on a desert or floodplain tile
Egypt's starting bias production deficit and the Sphynx weaknesses are adressed in one single swoop!
France
Grand Tour: In addition to the extra tourism, wonders provide extra appeal and +1 amenities to a radious of 3 surrounding tiles
This way, France UA's starts affecting the game since the very beggining by providing extra amenities for your nearby cities, while synergizing as well with its other boosted unique...
Chateau: Unlocks at Feudalism. Generates culture depending on its title's appeal. +1 gold per adjacent luxury resource
Earlier access to chateaus will make France more of a cultural powerhouse, while making its effects dependant on its terrain appeal will make for some truthly intersting set of decisions when deciding their placement.
Norway
Berserker is now a replacement for swordman rather than its own unit
This way, early agression could be far more viable for Norway due to the new upgrading path.
All current Norway's bonuses get transferred to Harald
Norway's UA: Strategic resource fund
You can build units everywhere with just one strategic resource (no need for an encampment or a second resource). +1 gold and +1 production in all your strategic land resources and on every sea resources hexes
Norway's weakness is so pronnounced that I think that an entire rework is in order. Norway's strategic fund will help it in order to wage war and to make more of a trading nation since it will be easy for her to sell their resource copies. On top of that, the gold and production bonuses to sea resources and land strategic resources will help to alliviate its weak coastatal starts.
USA
A faster rate of acquiring legacy bonuses for every civ will indirectly boost the USA's UA. If it ends up being unbalanced.