[RPG] Does an Outsider (Native) player character also get all the Bestiary Outsider features

but how would performing these almost surely evil acts affect how my character is expected to play the game from then on?

To me this is the most important thing you asked. The answer is: Not At All.

Your character appears to have a well-defined backstory and personalty. Those things define how your character should act. Alignment should reflect those, and that's all. Your alignment changing because of your actions should NOT affect how your character acts, as the alignment just shifted to reflect what you were already doing.

Don't fall into the trap of going "oh I got revenge and the DM made me evil, so now I'm throwing out my character's persona and going supervillan."

Alignment is there to help people who don't have a clear personality for characters, provide game mechanics for things like Smite Evil, and provide some restrictions that we could probably do without. It's not there to act as a straightjacket on what is a well-developed character.

Now, the actual act of getting revenge and fallout from that might cause your character to behave differently. That's RP and entirely in-bounds. If the party treats you differently afterwards that is going to have an effect, but the alignment system doesn't reflect that very well. (Parties can shun good aligned people too.)

How much should other players be aware of my plans?

Depends on the players, really. Are they players who will be okay with some manipulation and secrecy? Or are they players who really value team cohesion and won't appreciate being led around for a secret potentially evil plan?

There's not a good way for me to answer that, as you know them better than I do. I would say that your character probably won't tell them more than necessary unless he's sure that telling them would make them more willing to help.

How careful should I be about players' reactions to having my PC manipulate other PCs?

Same thing as above, really. Some players would have no problem with it at all, others would be rather unhappy.

If my character does manage to enact his revenge (and he may never finish doing so), assuming the actions are metaphysically evil (e.g., knowingly killing a good-aligned entity, etc.), does this make my character evil? What about the other PCs - are they evil? If not, do they turn on me?

While killing a Good creature like an Angel could be called an outright evil act, one evil act doesn't necessarily make you evil. Mortals almost never follow alignments perfectly, they're a mix of different acts and it's more the trend that determines it.

The other PCs may or may not have their own alignment trouble, depending on the situation. How much do they know about why they're helping you? How good are they usually?

And no, if they're helping you do this knowingly and your alignment shifts because of it, they shouldn't just automatically turn on you. That wouldn't make sense, would it?

Low stats do not mean low participation.

Just because a character does not have high numbers in a particular stat does not mean they cannot participate in any particular encounter. As someone who's played a 5e bard, the fact that you and your player think they're worthless in combat is baffling to me. Why are they only shooting a crossbow when they're arguably one of the most versatile casters in the game?

Likewise, just because your barbarian has low CHA and INT doesn't mean they can't interact with NPCs. I've seen (and played) characters who were obnoxious, dumb oafs that nevertheless manage to engage in entertaining social interactions. A low CHA does not mean that you're shy--it just means you might be bad at lying, for example.

Ultimately, a character is more than their character sheet--they (ideally) have personalities, motivations, and preferences beyond their specific stats. In fact, it's sometimes more fun to have characters that are really bad at things they like to do, like a talkative CHA 6 character.

Explain this to your players.

Your players need to understand that they do not need to be slotted into specific gameplay niches. Most social interactions, for instance, don't actually require rolling checks--your barbarian can still talk to bartenders and ask for information. Likewise, almost every class has something useful to do in combat! Because you say that your players are willing to play both combat and RP, you should emphasize to your players that their gameplay is not fully determined by their stats. Instead of asking themselves, "Who has the best stats to engage in this interaction?" they should be asking, "What would my character be doing in this situation?"

This problem is also partially due to the players' self-imposed limitations. For example, if the bard doesn't have damaging spells, then they're throwing that part of their class away. How would you react to a fighter that refused to use a weapon? Hence, you need your players to accept that they should build characters that are useful in your campaign. When I played a bard, the only damaging spells I really used were Vicious Mockery, Dissonant Whispers, and Fireball--the rest were utility spells, and it worked well.

Create situations where character abilities are relevant.

Once you have buy-in from your players, you should build scenarios and encounters where players' abilities are relevant.

For social encounters, you can build in checks that are not CHA based. PHB 175 describes this variant:

Normally, your proficiency in a skill applies only to a specific kind of ability check... In some situations, though, your proficiency might reasonably apply to a different kind of check.

Therefore, your barbarian might be able to roll a Strength(intimidation) check to intimidate an NPC with a feat of strength, or a Constitution(performance) check to win a drinking game.

On the combat side, you can introduce intelligent enemies that will negotiate with the PCs during a combat. I've played and run a number of encounters that were half combat and half conversation--the skill monkey could play tricks that cause goblins to run away in fear, for example.

You'll have to be careful not to overuse these "crossover" tricks, lest you devalue the other side, but they're a useful tool to allow talkers to participate in combat and combatants to participate in talking.