Is it ready to play yet ?

Well, dunno what platform you're on, but I'm on my third playthrough so I guess it's at least reasonably playable.

There's no Keep. The extent of the "carryover" is choosing Shepard's gender. I don't think even that has any impact on dialogue.

As for mods, I know at least there's an appearance mod since people are dissatisfied with the character creator.

I don't know about the DRM stuff, but once you leave the CC that character's appearance is committed (unless you can mod the character post-creation).

It's a lot better. There are still a noticeable number of bugs and glitches, but I think most of the game breaking ones are fixed.

Some bugs have been fixed.
Yet be aware each bug that is fixed may lead to other bugs that are found an need fixing.
So far from what I see of the game at version 1.07 the main bugs that people complained about: the facial animations, black screen and other major ones have been fixed.
Check the trouble-shooting thread if you want to that showcases many bugs that have or may be solved.

As to mods... yes there is mods and it is beginning to grow.
There is even a ME:A Explorer- though in the early phases yet... Warranty Voider's work (Yep. One and the same.)
There are some mods currently that remove subtile annoyances that people have...
For instance the mod that gives a better camera angle over all or the mod to Shut. Sam. Up. or the more skill mod.
Aside from these casual tweaks the majority (not all) are game sames or character designs.
Texture modifications are beginning to be seen on the horizon... maybe mesh mods and what not will soon follow.
A lot of the current mods though may not yet be 1.07 ready.
Some mods like the inventory one should be though.
So far the modding is progressing and beginning to build but nothing gaming changing at current.

As to the DRM...
Don't get me started with Origin... -I hate that crap with a vengeance: 2+months trying to get ME:A to work -fixed now.
That said the game will only launch if you have Origin on your computer and running -though can be disable from the origin in program options.
Furthermore there are no manual saves on main mission worlds -all via checkpoints (there is a way to side step this - but does not always work.
However when not on a prime mission there was at least in 1.05 manual saves.

It is true that the CC is quite limited but since 1.06 at least it is better and there are at least two mods that allow usage of lighter skin and changing the presets you can start with. Also as KaiserShep has said there is no way currently to change character once you leave the character creator... maybe with a future DLC that may change but not currently. Still using a default Ryder appearance as a custom (at least female -still need to work on to get male custom to look like default Ryder.

Hope this is of help.

I mean, it's still a bit hit and miss on whether you'll have a smooth or glitchy experience. But I'd say you're 75% likely to have a decent experience, now.

Note: this is referring to game breaking bugs. The unpolished stuff is still unpolished. I won't sway you by mentioning specifics.

It's definitely much better, but ultimately down to your luck. I'm experiencing an almost bugless second walkthrough, while others still report a myriad of problems. Given that the last patch (and hotfix) is still recent, it'll surely take a while until the next one, so I'd say go for it.

Keep your eye on the Nexus for mods.

Wait until the June patch comes out first. It's said to bring more options to the lousy character creation tool. Once that is fixed i believe the game will be fully playable

Played it from day one (250 hours).
No significant issues that merited waiting in my view.

That's the rumor, apparently.

That's even if they announce story DLC in the future.