needs a bump!!

Bump because Leona is the best.

LOVE the idea of Adding effects to her spells if they're affected by sunlight.

That way she has some way of "Procing" her own passive. Also gives a reason to maybe change up her combo everyonce in a while rather then same W (before fight) E->Q->Wburst combo.

BUMP

Buff Eclipse's AP ratio/buff scaling.
I agree with this change, but nothing over the top. I think a 45% ratio can work.

Lower Eclipse's cooldown.
Maybe? If they made the cooldown decrease with the skill level I can see this working.
Leona's cooldowns are fairly short. Especially her ultimate. If you build some CDR somewhere, you benefit a lot from the cooldowns. Especially if you have CDR masteries.

Increasing the stun radius of Solar Flare
No. The range on this stun is decent. You must land the stun with good timing.
Poor use punishes you, while good use rewards you.

Changing Leona's E to a stun.
NO. She already has the potential to lockdown a single target for 3.25 seconds. That is an incredibly long time in a fight. This would be unbalanced.

Increasing Leona's Q stun duration
Again, no. See above.

Have Leona's Q stun duration scale (1/1.25/1.5/1.75/2)
I like the idea of having the stun scale, but again you run into total stun duration. I have to disagree with this.

Buff Leona's Q AP ratio
Yes, but not that high. 35% or 40% works.

Give Leona some more health and health regeneration per level
No.
That's what runes and items are for. You need to make a tradeoff somewhere.
Also, go look into her base health regen stats and per level stats. Its one of the highest in the game. You don't seem to understand champion balance.
http://leagueoflegends.wikia.com/wiki/List_of_champion's_Health_Regeneration

Edit.
Wanted to make a comment on her passive.
Allow her to proc her passive on minions. She cannot proc the passive on champions.
I think that the following change can help her farm minions, as well as give her potential to be a solo champion.

Although this may pose the problem of giving her jungle viability. Although this isn't really a bad thing, she isn't totally meant for this role. I love the idea of her ganking lanes, and her abilities suite really well for this.

If we're talking about champion roles, say in terms of junglers, Riot has been trying to make it easier for different types of jungling champions. This can potentially lead to champions who are normally not played in jungle roles. Such as AP champions, which Riot has commented on.
I would love to see a Leona jungle work. Break ze meta!

I do, and I don't agree with that. She isn't meant to be a duelist, but that can always change.
I mean people have done solo mids with Leona, but I don't think it's something that works often enough for it to be viable.

So lets say for curiosity she does have the ability to proc it herself, on everything. Now she can go anywhere. Now what? Do you throw her top? Why? Just because you can? How would that even be viable againts normal Top laners, verus Olaf, Irelia, Singed, etc.
Do you start roaming if your ahead? or just tower camp if you get behind? That offers little to a team composition, and is doing more harm than good.

Now lets say for example you send Leona mid. Sure she can have a hard time against most normal AP mids, especially if they have ranged basic attacks. You are going to farm with W and E, and stun with Q if anything happens. You might have the possibility to roam. You also have great opportunity to lock down a champion, but i don't think Leona would have enough burst damage to finish anyone off. The AP scaling isn't meant for that. Again, I think she can get outplayed a lot by most AP mids.

Now lets say she can jungle. She has great ability to clear with the AoE, and her W gives her some more resistances. She is going to be heavily mana dependent though. Her mana costs and cooldown may force one to use good timing on skills and procing the passive.

Now what can she do? She can start ganks. At level 3 she has very high presence. Her range on Zenith Blade is very good. You have to land the ability though, to have a chance of getting a successful gank. Otherwise you need to sneak in from behind if that fails, and walk up for the stun. Hope the enemy burns a flash, and comeback in a few seconds. The only downside I can see is her mobility. You would need to spec masteries or runes a little bit, and this can help with traveling between camps. Speed will also help geting to a lane faster, so there is less time wasted in walking. You also don't want to be spending too much time camping a lane, as with any jungler.