By RAW: you can use a dart with Defensive Duelist. It just asks for a finesse weapon, not necessarily a melee weapon.
However, personally I would rule that it would require a finesse melee weapon, and I imagine it would probably be changed in a future version of the Errata to specify finesse melee weapons. Darts just aren't something you'd expect someone to even attempt to deflect a blow with.
It's already been pointed out that your question is perhaps a little too broad. So you may want to edit and narrow it down.
However, I'll focus my answer on a specific paragraph which seems to be your biggest concern:
I am the primary tank of the team so I need my AC high. In the adventures however, there seems to be so many opponents I soak up (usually 3 at a time engaging) that I am almost in low health before we win.
Tanking is not purely about AC. And if you obsess about this single aspect it will hamper your effectiveness.
An important aspect of tanking is control.
- When fighting unintelligent creatures, it may be easy enough to put yourself front and centre and they'll attack you. But more intelligent opponents may choose to ignore you and attack "better" targets instead. Champions tend to be focused more on raw power, so you'll have to rely on your teammates to cover this.
- But you might want to consider the Protection fighting style, which defends nearby allies by imposing disadvantage on an enemies attack roll.
- Sentinel is a good choice of feat.
- Mobile can be a useful feat making it safer to move around during combat.
AC suffers diminishing returns
Basically + 1 AC reduces average damage per attack by less for each point gained. The reasons are:
- Natural 20 is a guaranteed hit (+1 AC may in extreme cases may have zero effect of the range of rolls that succeed or miss).
- The critical effect boosts damage of a high roll (so AC increases reduce average damage / attack by less for each point).
Something that can be far more effective is imposing disadvantage or removing advantage.
At the extreme end, if an enemy needs to roll 20 to hit: +1 AC has zero effect on the odds of doing damage. But disadvantage reduces the odds from 1 in 20 to 1 in 400. And removing advantage reduces the odds from just under 1 in 10 to 1 in 20.
The benefit of AC is that it's passive. It's "always on" and available to avoid damage. It doesn't get "used up" and doesn't consume actions.
However, something seriously worth considering in place of a small AC boost is the Lucky feat.
AC doesn't help at all in some situations
Many magic attacks don't require an attack roll, meaning AC is useless. So you may want to consider alternative forms of damage avoidance.
- Shield Master is an excellent choice.
- Again the Lucky feat is noteworthy.
(Though I'm a little skeptical of the benefits of the Resilient feat.)
That said, unless you're in a very heavily combat and tactics focused group, you shouldn't need to min/max your abilities. In combat, teamwork and cooperation are far more important. And there's plenty that goes on in the game outside of combat.
Best Answer
Shield has a somatic component and you only have one reaction per round
Everything else works though. Just to run though the list; wearing studded armour sets your AC to 12 + your Dexterity modifier of 3. In one hand you hold a shield which adds +2 and in the other you hold a finesse weapon with which Defensive duelist can add a bonus equal to your proficiency (ie. +2) as a reaction for a given attack. However, both your hands are occupied meaning you have none left to provide the somatic component (S) of shield. Also, you have used your reaction with Defensive duelist, which means you haven't got it available to also cast shield.
You can of course solve the first issue by picking up the Warcaster feat using its second benefit:
At which point you will have to choose between using shield and Defensive duelist. Note that the bonus to AC from shield will be higher until you reach 13th level, but does cost one of your precious spell slots. Shield does however work until the start of your next turn, and not just on the singular attack.