There are not.
The benefit of a romance with a fey is unique to that feat, as is the +2 bonus to all Charisma-based checks.
Being regarded as fey can be obtained by being fey, and you can get that from various prestige classes as well as the spirit shaman base class, but in all cases this benefit is a capstone, which is quire pricey, and it doesn’t exist in feat form. Counting as fey for interaction doesn’t appear to exist anywhere but Nymph’s Kiss.
The +1 bonus on saving throws against all spells and spell-like abilities is very broad; Divine Spellshield can actually do twice that, for your whole party, but it’s not permanent: it requires you to spend a daily use of rebuke earth to get \$level\$ rounds of it. Otherwise, you can get bonuses against a much narrower band of abilities.
You also cannot get a skill point per level from any other feat. In fact, very few feats touch skill points at all.
- Open Minded is a one-time bonus of 5 skill points.
- Human Heritage from Races of Destiny is a one-time bonus of 4 skill points (and grants you the Humanoid type and Human subtype). Requires being half-human.
- Apprentice from Dungeon Master’s Guide II gives you a one-time bonus of 2 skill points, but they must be spent on the skills associated with your apprenticeship (which, more usefully, become permanent class skills for you).
Beyond these, I am not aware of any feats that help you.
It is unclear what you mean by your DM getting picky about the relationship with a fey thing, but it may be worth reminding him that said relationship is mentioned as part of the Benefit section of the feat. It is not a requirement. That means that, as far as the mechanics of the feat are concerned, the relationship is another thing you are supposed to get out of it, not something you have to maintain in order to keep the feat. It can very easily be ignored—in theory, it means the character who takes the feat gets less out of it than they would as written.
And while Nymph’s Kiss is a quite-good feat, feats are massively valuable, and skill points are largely not. Particularly at 1st level, when it may be the only feat you get.
As for Exalted, it was a bad idea and poorly written. In general, Book of Exalted Deeds was a bad idea and poorly written—Nymph’s Kiss is one of very few things in it worth salvaging. I recommend treating a Good character as good enough for Exalted—the “extra-Good” concept just isn’t interesting or meaningful, Good already existed for the concept of a good character. For that matter, I see no reason why the benefits of Nymph’s Kiss ought to be restricted by alignment in the first place—but then I generally ignore alignment entirely since it, too, is a bad idea and poorly written.